%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU678^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:04 EDT 2024
% Result : Theorem 3.53s 1.01s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 281
% Syntax : Number of formulae : 401 ( 43 unt; 237 typ; 0 def)
% Number of atoms : 1510 ( 197 equ; 0 cnn)
% Maximal formula atoms : 366 ( 9 avg)
% Number of connectives : 4560 ( 205 ~; 265 |; 296 &;3164 @)
% ( 54 <=>; 576 =>; 0 <=; 0 <~>)
% Maximal formula depth : 363 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 210 ( 210 >; 0 *; 0 +; 0 <<)
% Number of symbols : 241 ( 237 usr; 201 con; 0-4 aty)
% Number of variables : 757 ( 156 ^ 552 !; 49 ?; 757 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_253,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_254,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_255,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_256,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_257,type,
esk6_2: $i > ( $i > $o ) > $i ).
thf(decl_258,type,
esk7_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_259,type,
esk8_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_260,type,
esk9_2: $i > ( $i > $o ) > $i ).
thf(decl_261,type,
esk10_2: $i > ( $i > $o ) > $i ).
thf(decl_262,type,
esk11_2: $i > ( $i > $o ) > $i ).
thf(decl_263,type,
esk12_1: $i > $i ).
thf(decl_264,type,
esk13_1: $i > $i ).
thf(decl_265,type,
esk14_3: $i > $i > $i > $i ).
thf(decl_266,type,
esk15_4: $i > $i > $i > $i > $i ).
thf(decl_267,type,
esk16_3: $i > $i > $i > $i ).
thf(decl_268,type,
esk17_3: $i > $i > $i > $i ).
thf(decl_269,type,
esk18_4: $i > $i > $i > $i > $i ).
thf(decl_270,type,
esk19_3: $i > $i > $i > $i ).
thf(decl_271,type,
esk20_0: $i ).
thf(decl_272,type,
esk21_0: $i ).
thf(decl_273,type,
esk22_0: $i > $i ).
thf(decl_274,type,
esk23_0: $i ).
thf(decl_275,type,
epred1_0: $i > $i > $o ).
thf(decl_276,type,
epred2_0: $i > $o ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
& ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ex1 @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(lamProp,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X31 @ X2 )
= X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(c_0_40,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X156: $i] :
( ( in @ X156
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X156 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_41,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_42,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X163: $i] :
( ( in @ X163
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X163 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_43,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_44,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X156: $i] :
( ( in @ X156
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X156 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_45,plain,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ksndsingleton]) ).
thf(c_0_46,plain,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_47,plain,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singletonprop]) ).
thf(c_0_48,plain,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_49,plain,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I]) ).
thf(c_0_50,plain,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E1]) ).
thf(c_0_51,plain,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[setOfPairsIsBReln]) ).
thf(c_0_52,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X163: $i] :
( ( in @ X163
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X163 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
thf(c_0_53,plain,
( apProp
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
@ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[apProp]) ).
thf(c_0_54,plain,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_55,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X162: $i] :
( ( in @ X162
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X162 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_45,c_0_41]) ).
thf(c_0_56,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X161: $i] :
( ( in @ X161 @ X21 )
& ( X21
= ( setadjoin @ X161 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_41]) ).
thf(c_0_57,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X160: $i] :
( ( in @ X160
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X160 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_46,c_0_41]) ).
thf(c_0_58,plain,
( singletonprop
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ? [X155: $i] :
( ( in @ X155
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X155 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_47,c_0_41]) ).
thf(c_0_59,plain,
( ex1I2
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ? [X159: $i] :
( ( in @ X159
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X159 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_48,c_0_44]) ).
thf(c_0_60,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X158: $i] :
( ( in @ X158
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X158 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_49,c_0_44]) ).
thf(c_0_61,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X157: $i] :
( ( in @ X157
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X157 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_50,c_0_44]) ).
thf(c_0_62,plain,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X28 @ Z0 @ Z1 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrER]) ).
thf(c_0_63,plain,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X27 @ Z0 @ Z1 ) ) )
=> ( in @ X3 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL2]) ).
thf(c_0_64,plain,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X26 @ Z0 @ Z1 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL1]) ).
thf(c_0_65,plain,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X25 @ Z0 @ Z1 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrERa]) ).
thf(c_0_66,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_51,c_0_43]) ).
thf(c_0_67,plain,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X23 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrSub]) ).
thf(c_0_68,plain,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X22 @ Z0 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrI]) ).
thf(c_0_69,axiom,
( funcinfuncset
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X173: $i] :
( ( in @ X173 @ X4 )
=> ? [X174: $i] :
( ( in @ X174
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X173 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X173 @ Z0 ) @ X30 ) )
= ( setadjoin @ X174 @ emptyset ) ) ) ) )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcinfuncset,c_0_52]) ).
thf(c_0_70,axiom,
( infuncsetfunc
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X171: $i] :
( ( in @ X171 @ X4 )
=> ? [X172: $i] :
( ( in @ X172
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X171 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X171 @ Z0 ) @ X30 ) )
= ( setadjoin @ X172 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[infuncsetfunc,c_0_52]) ).
thf(c_0_71,axiom,
( app
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X169: $i] :
( ( in @ X169 @ X4 )
=> ? [X170: $i] :
( ( in @ X170
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X169 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X169 @ Z0 ) @ X30 ) )
= ( setadjoin @ X170 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[app,c_0_52]) ).
thf(c_0_72,plain,
( apProp
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X167: $i] :
( ( in @ X167 @ X4 )
=> ? [X168: $i] :
( ( in @ X168
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X167 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X167 @ Z0 ) @ X30 ) )
= ( setadjoin @ X168 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
@ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_53,c_0_52]) ).
thf(c_0_73,plain,
( funcImageSingleton
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X164: $i] :
( ( in @ X164 @ X4 )
=> ? [X165: $i] :
( ( in @ X165
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X164 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X164 @ Z0 ) @ X30 ) )
= ( setadjoin @ X165 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X166: $i] :
( ( in @ X166
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) )
= ( setadjoin @ X166 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_54,c_0_52]),c_0_41]) ).
thf(c_0_74,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( ! [X175: $i,X176: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X175 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X175 @ ( setadjoin @ X176 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X177: $i,X178: $i] : ( iskpair @ ( kpair @ X177 @ X178 ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( ! [X179: $i,X180: $i,X181: $i] :
( ( in @ X181 @ X179 )
=> ! [X182: $i] :
( ( in @ X182 @ X180 )
=> ( in @ ( kpair @ X181 @ X182 ) @ ( cartprod @ X179 @ X180 ) ) ) )
=> ( ! [X183: $i,X184: $i,X185: $i] :
( ( in @ X185 @ ( cartprod @ X183 @ X184 ) )
=> ? [X186: $i] :
( ( in @ X186 @ X183 )
& ? [X187: $i] :
( ( in @ X187 @ X184 )
& ( X185
= ( kpair @ X186 @ X187 ) ) ) ) )
=> ( ! [X188: $i,X189: $i,X190: $i] :
( ( in @ X190 @ ( cartprod @ X188 @ X189 ) )
=> ( iskpair @ X190 ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X191: $i,X192: $i > $o] :
( ! [X193: $i] :
( ( in @ X193 @ X191 )
=> ! [X194: $i] :
( ( in @ X194 @ X191 )
=> ( ( X192 @ X193 )
=> ( ( X192 @ X194 )
=> ( X193 = X194 ) ) ) ) )
=> ( ? [X195: $i] :
( ( in @ X195 @ X191 )
& ( X192 @ X195 ) )
=> ? [X196: $i] :
( ( in @ X196 @ ( dsetconstr @ X191 @ X192 ) )
& ( ( dsetconstr @ X191 @ X192 )
= ( setadjoin @ X196 @ emptyset ) ) ) ) )
=> ( ! [X197: $i,X198: $i > $o] :
( ? [X199: $i] :
( ( in @ X199 @ ( dsetconstr @ X197 @ X198 ) )
& ( ( dsetconstr @ X197 @ X198 )
= ( setadjoin @ X199 @ emptyset ) ) )
=> ? [X200: $i] :
( ( in @ X200 @ X197 )
& ( X198 @ X200 ) ) )
=> ( ! [X201: $i,X202: $i > $o,X203: $i] :
( ( in @ X203 @ X201 )
=> ( ( X202 @ X203 )
=> ( ! [X204: $i] :
( ( in @ X204 @ X201 )
=> ( ( X202 @ X204 )
=> ( X204 = X203 ) ) )
=> ? [X205: $i] :
( ( in @ X205 @ ( dsetconstr @ X201 @ X202 ) )
& ( ( dsetconstr @ X201 @ X202 )
= ( setadjoin @ X205 @ emptyset ) ) ) ) ) )
=> ( ! [X206: $i,X207: $i > $o] :
( ! [X208: $i] :
( ( in @ X208 @ X206 )
=> ! [X209: $i] :
( ( in @ X209 @ X206 )
=> ( ( X207 @ X208 )
=> ( ( X207 @ X209 )
=> ( X208 = X209 ) ) ) ) )
=> ( ? [X210: $i] :
( ( in @ X210 @ X206 )
& ( X207 @ X210 ) )
=> ? [X211: $i] :
( ( in @ X211 @ ( dsetconstr @ X206 @ X207 ) )
& ( ( dsetconstr @ X206 @ X207 )
= ( setadjoin @ X211 @ emptyset ) ) ) ) )
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X212: $i] :
( ( iskpair @ X212 )
=> ? [X213: $i] :
( ( in @ X213
@ ( dsetconstr @ ( setunion @ X212 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X212 ) ) )
& ( ( dsetconstr @ ( setunion @ X212 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X212 ) )
= ( setadjoin @ X213 @ emptyset ) ) ) )
=> ( ! [X214: $i] :
( ? [X215: $i] :
( ( in @ X215 @ X214 )
& ( X214
= ( setadjoin @ X215 @ emptyset ) ) )
=> ( in @ ( setunion @ X214 ) @ X214 ) )
=> ( ! [X216: $i,X217: $i] :
( ( kfst @ ( kpair @ X216 @ X217 ) )
= X216 )
=> ( ! [X218: $i,X219: $i,X220: $i] :
( ( in @ X220 @ ( cartprod @ X218 @ X219 ) )
=> ( in @ ( kfst @ X220 ) @ X218 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X221: $i] :
( ( iskpair @ X221 )
=> ? [X222: $i] :
( ( in @ X222
@ ( dsetconstr @ ( setunion @ X221 )
@ ^ [Z0: $i] :
( X221
= ( kpair @ ( kfst @ X221 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X221 )
@ ^ [Z0: $i] :
( X221
= ( kpair @ ( kfst @ X221 ) @ Z0 ) ) )
= ( setadjoin @ X222 @ emptyset ) ) ) )
=> ( ! [X223: $i,X224: $i] :
( ( ksnd @ ( kpair @ X223 @ X224 ) )
= X224 )
=> ( ! [X225: $i] :
( ( iskpair @ X225 )
=> ( ( kpair @ ( kfst @ X225 ) @ ( ksnd @ X225 ) )
= X225 ) )
=> ( ! [X226: $i,X227: $i,X228: $i] :
( ( in @ X228 @ ( cartprod @ X226 @ X227 ) )
=> ( in @ ( ksnd @ X228 ) @ X227 ) )
=> ( ! [X229: $i,X230: $i,X231: $i,X232: $i] :
( ( in @ ( kpair @ X231 @ X232 ) @ ( cartprod @ X229 @ X230 ) )
=> ( in @ X231 @ X229 ) )
=> ( ! [X233: $i,X234: $i,X235: $i,X236: $i] :
( ( in @ ( kpair @ X235 @ X236 ) @ ( cartprod @ X233 @ X234 ) )
=> ( in @ X236 @ X234 ) )
=> ( cartprodmempaircEq
=> ( ! [X237: $i,X238: $i,X239: $i] :
( ( in @ X239 @ X237 )
=> ! [X240: $i] :
( ( in @ X240 @ X238 )
=> ( ( kfst @ ( kpair @ X239 @ X240 ) )
= X239 ) ) )
=> ( ! [X241: $i,X242: $i,X243: $i] :
( ( in @ X243 @ X241 )
=> ! [X244: $i] :
( ( in @ X244 @ X242 )
=> ( ( ksnd @ ( kpair @ X243 @ X244 ) )
= X244 ) ) )
=> ( ! [X245: $i,X246: $i,X247: $i] :
( ( in @ X247 @ ( cartprod @ X245 @ X246 ) )
=> ( ( kpair @ ( kfst @ X247 ) @ ( ksnd @ X247 ) )
= X247 ) )
=> ( ! [X248: $i,X249: $i,X250: $i > $i > $o,X251: $i] :
( ( in @ X251 @ X248 )
=> ! [X252: $i] :
( ( in @ X252 @ X249 )
=> ( ( X250 @ X251 @ X252 )
=> ( in @ ( kpair @ X251 @ X252 ) @ ( dpsetconstr @ X248 @ X249 @ X250 ) ) ) ) )
=> ( ! [X253: $i,X254: $i,X255: $i > $i > $o] : ( subset @ ( dpsetconstr @ X253 @ X254 @ X255 ) @ ( cartprod @ X253 @ X254 ) )
=> ( ! [X256: $i,X257: $i,X258: $i > $i > $o] : ( subset @ ( dpsetconstr @ X256 @ X257 @ X258 ) @ ( cartprod @ X256 @ X257 ) )
=> ( ! [X259: $i,X260: $i,X261: $i > $i > $o,X262: $i] :
( ( in @ X262 @ X259 )
=> ! [X263: $i] :
( ( in @ X263 @ X260 )
=> ( ( in @ ( kpair @ X262 @ X263 ) @ ( dpsetconstr @ X259 @ X260 @ X261 ) )
=> ( X261 @ X262 @ X263 ) ) ) )
=> ( ! [X264: $i,X265: $i,X266: $i > $i > $o,X267: $i,X268: $i] :
( ( in @ ( kpair @ X267 @ X268 ) @ ( dpsetconstr @ X264 @ X265 @ X266 ) )
=> ( in @ X267 @ X264 ) )
=> ( ! [X269: $i,X270: $i,X271: $i > $i > $o,X272: $i,X273: $i] :
( ( in @ ( kpair @ X272 @ X273 ) @ ( dpsetconstr @ X269 @ X270 @ X271 ) )
=> ( in @ X273 @ X270 ) )
=> ( ! [X274: $i,X275: $i,X276: $i > $i > $o,X277: $i,X278: $i] :
( ( in @ ( kpair @ X277 @ X278 ) @ ( dpsetconstr @ X274 @ X275 @ X276 ) )
=> ( X276 @ X277 @ X278 ) )
=> ( ! [X279: $i,X280: $i,X281: $i] :
( ( ( subset @ X281 @ ( cartprod @ X279 @ X280 ) )
& ! [X282: $i] :
( ( in @ X282 @ X279 )
=> ? [X283: $i] :
( ( in @ X283
@ ( dsetconstr @ X280
@ ^ [Z0: $i] : ( in @ ( kpair @ X282 @ Z0 ) @ X281 ) ) )
& ( ( dsetconstr @ X280
@ ^ [Z0: $i] : ( in @ ( kpair @ X282 @ Z0 ) @ X281 ) )
= ( setadjoin @ X283 @ emptyset ) ) ) ) )
=> ! [X284: $i] :
( ( in @ X284 @ X279 )
=> ? [X285: $i] :
( ( in @ X285
@ ( dsetconstr @ X280
@ ^ [Z0: $i] : ( in @ ( kpair @ X284 @ Z0 ) @ X281 ) ) )
& ( ( dsetconstr @ X280
@ ^ [Z0: $i] : ( in @ ( kpair @ X284 @ Z0 ) @ X281 ) )
= ( setadjoin @ X285 @ emptyset ) ) ) ) )
=> ( ! [X286: $i,X287: $i,X288: $i] :
( ( ( subset @ X288 @ ( cartprod @ X286 @ X287 ) )
& ! [X289: $i] :
( ( in @ X289 @ X286 )
=> ? [X290: $i] :
( ( in @ X290
@ ( dsetconstr @ X287
@ ^ [Z0: $i] : ( in @ ( kpair @ X289 @ Z0 ) @ X288 ) ) )
& ( ( dsetconstr @ X287
@ ^ [Z0: $i] : ( in @ ( kpair @ X289 @ Z0 ) @ X288 ) )
= ( setadjoin @ X290 @ emptyset ) ) ) ) )
=> ! [X291: $i] :
( ( in @ X291 @ X286 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X287
@ ^ [Z0: $i] : ( in @ ( kpair @ X291 @ Z0 ) @ X288 ) ) )
@ X287 ) ) )
=> ( ! [X292: $i,X293: $i,X294: $i] :
( ( ( subset @ X294 @ ( cartprod @ X292 @ X293 ) )
& ! [X295: $i] :
( ( in @ X295 @ X292 )
=> ? [X296: $i] :
( ( in @ X296
@ ( dsetconstr @ X293
@ ^ [Z0: $i] : ( in @ ( kpair @ X295 @ Z0 ) @ X294 ) ) )
& ( ( dsetconstr @ X293
@ ^ [Z0: $i] : ( in @ ( kpair @ X295 @ Z0 ) @ X294 ) )
= ( setadjoin @ X296 @ emptyset ) ) ) ) )
=> ! [X297: $i] :
( ( in @ X297 @ X292 )
=> ( in @ ( ap @ X292 @ X293 @ X294 @ X297 ) @ X293 ) ) )
=> ( ! [X298: $i,X299: $i,X300: $i] :
( ( in @ X300 @ ( funcSet @ X298 @ X299 ) )
=> ( ( subset @ X300 @ ( cartprod @ X298 @ X299 ) )
& ! [X301: $i] :
( ( in @ X301 @ X298 )
=> ? [X302: $i] :
( ( in @ X302
@ ( dsetconstr @ X299
@ ^ [Z0: $i] : ( in @ ( kpair @ X301 @ Z0 ) @ X300 ) ) )
& ( ( dsetconstr @ X299
@ ^ [Z0: $i] : ( in @ ( kpair @ X301 @ Z0 ) @ X300 ) )
= ( setadjoin @ X302 @ emptyset ) ) ) ) ) )
=> ( ! [X303: $i,X304: $i,X305: $i] :
( ( in @ X305 @ ( funcSet @ X303 @ X304 ) )
=> ! [X306: $i] :
( ( in @ X306 @ X303 )
=> ( in @ ( ap @ X303 @ X304 @ X305 @ X306 ) @ X304 ) ) )
=> ( ! [X307: $i,X308: $i,X309: $i] :
( ( ( subset @ X309 @ ( cartprod @ X307 @ X308 ) )
& ! [X310: $i] :
( ( in @ X310 @ X307 )
=> ? [X311: $i] :
( ( in @ X311
@ ( dsetconstr @ X308
@ ^ [Z0: $i] : ( in @ ( kpair @ X310 @ Z0 ) @ X309 ) ) )
& ( ( dsetconstr @ X308
@ ^ [Z0: $i] : ( in @ ( kpair @ X310 @ Z0 ) @ X309 ) )
= ( setadjoin @ X311 @ emptyset ) ) ) ) )
=> ( in @ X309 @ ( funcSet @ X307 @ X308 ) ) )
=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( ( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i] : ( $eq @ ( X31 @ Z0 ) ) )
@ ( cartprod @ X4 @ X5 ) )
& ! [X312: $i] :
( ( in @ X312 @ X4 )
=> ? [X313: $i] :
( ( in @ X313
@ ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X312 @ Z0 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z1: $i] : ( $eq @ ( X31 @ Z1 ) ) ) ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X312 @ Z0 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z1: $i] : ( $eq @ ( X31 @ Z1 ) ) ) ) )
= ( setadjoin @ X313 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[lamProp])]),c_0_52]),cartprodsndpairEq]),ksndpairEq]),cartprodfstpairEq]),kfstpairEq]),kpairsurjEq]),kpairp]),kpairiskpair]),cartprodpairsurjEq]),cartprodpairmemER]),cartprodpairmemEL]),cartprodsndin]),cartprodfstin]),cartprodmempair]),cartprodmempair1]),cartprodpairin]),ap2p]),c_0_55]),c_0_56]),c_0_57]),c_0_58]),c_0_59]),c_0_60]),c_0_61]),c_0_62]),c_0_63]),c_0_64]),c_0_65]),c_0_66]),c_0_67]),c_0_68]),c_0_69]),c_0_70]),c_0_71]),c_0_72]),c_0_73])]) ).
thf(c_0_75,negated_conjecture,
! [X318: $i,X319: $i,X320: $i,X321: $i,X322: $i,X323: $i,X324: $i,X325: $i,X326: $i,X327: $i,X328: $i,X331: $i,X332: $i,X333: $i,X334: $i,X335: $i > $o,X338: $i,X340: $i,X341: $i > $o,X342: $i,X344: $i,X345: $i > $o,X346: $i,X349: $i,X350: $i > $o,X353: $i,X355: $i,X357: $i,X358: $i,X359: $i,X360: $i,X361: $i,X362: $i,X363: $i,X364: $i,X366: $i,X367: $i,X368: $i,X369: $i,X370: $i,X371: $i,X372: $i,X373: $i,X374: $i,X375: $i,X376: $i,X377: $i,X378: $i,X379: $i,X380: $i,X381: $i,X382: $i,X383: $i,X384: $i,X385: $i,X386: $i,X387: $i,X388: $i,X389: $i,X390: $i,X391: $i,X392: $i,X393: $i > $i > $o,X394: $i,X395: $i,X396: $i,X397: $i,X398: $i > $i > $o,X399: $i,X400: $i,X401: $i > $i > $o,X402: $i,X403: $i,X404: $i > $i > $o,X405: $i,X406: $i,X407: $i,X408: $i,X409: $i > $i > $o,X410: $i,X411: $i,X412: $i,X413: $i,X414: $i > $i > $o,X415: $i,X416: $i,X417: $i,X418: $i,X419: $i > $i > $o,X420: $i,X421: $i,X422: $i,X423: $i,X424: $i,X426: $i,X427: $i,X429: $i,X430: $i,X431: $i,X433: $i,X434: $i,X435: $i,X436: $i,X437: $i,X439: $i,X440: $i,X441: $i,X442: $i,X443: $i,X444: $i,X446: $i,X447: $i,X448: $i,X449: $i,X450: $i,X451: $i,X452: $i,X454: $i,X458: $i,X460: $i] :
( setextAx
& emptysetAx
& setadjoinAx
& powersetAx
& setunionAx
& omega0Ax
& omegaSAx
& omegaIndAx
& replAx
& foundationAx
& wellorderingAx
& descrp
& dsetconstrI
& dsetconstrEL
& dsetconstrER
& exuE1
& prop2setE
& emptysetE
& emptysetimpfalse
& notinemptyset
& exuE3e
& setext
& emptyI
& noeltsimpempty
& setbeta
& nonemptyE1
& nonemptyI
& nonemptyI1
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& setoftrueEq
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& setunionI
& setunionE
& subPowSU
& exuE2
& nonemptyImpWitness
& uniqinunit
& notinsingleton
& eqinunit
& singletonsswitch
& upairsetE
& upairsetIL
& upairsetIR
& emptyE1
& vacuousDall
& quantDeMorgan1
& quantDeMorgan2
& quantDeMorgan3
& quantDeMorgan4
& prop2setI
& prop2set2propI
& notdexE
& notdallE
& exuI1
& exuI3
& exuI2
& inCongP
& in__Cong
& exuE3u
& exu__Cong
& emptyset__Cong
& setadjoin__Cong
& powerset__Cong
& setunion__Cong
& omega__Cong
& exuEu
& descr__Cong
& dsetconstr__Cong
& subsetI1
& eqimpsubset2
& eqimpsubset1
& subsetI2
& emptysetsubset
& subsetE
& subsetE2
& notsubsetI
& notequalI1
& notequalI2
& subsetRefl
& subsetTrans
& setadjoinSub
& setadjoinSub2
& subset2powerset
& setextsub
& subsetemptysetimpeq
& powersetI1
& powersetE1
& inPowerset
& powersetsubset
& sepInPowerset
& sepSubset
& binunionIL
& upairset2IR
& binunionIR
& binunionEcases
& binunionE
& binunionLsub
& binunionRsub
& binintersectI
& binintersectSubset5
& binintersectEL
& binintersectLsub
& binintersectSubset2
& binintersectSubset3
& binintersectER
& disjointsetsI1
& binintersectRsub
& binintersectSubset4
& binintersectSubset1
& bs114d
& setminusI
& setminusEL
& setminusER
& setminusSubset2
& setminusERneg
& setminusELneg
& setminusILneg
& setminusIRneg
& setminusLsub
& setminusSubset1
& symdiffE
& symdiffI1
& symdiffI2
& symdiffIneg1
& symdiffIneg2
& secondinupair
& setukpairIL
& setukpairIR
& ( iskpair @ ( setadjoin @ ( setadjoin @ X318 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X318 @ ( setadjoin @ X319 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X320 @ X321 ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& ( ~ ( in @ X324 @ X322 )
| ~ ( in @ X325 @ X323 )
| ( in @ ( kpair @ X324 @ X325 ) @ ( cartprod @ X322 @ X323 ) ) )
& ( ( in @ ( esk1_3 @ X326 @ X327 @ X328 ) @ X326 )
| ~ ( in @ X328 @ ( cartprod @ X326 @ X327 ) ) )
& ( ( in @ ( esk2_3 @ X326 @ X327 @ X328 ) @ X327 )
| ~ ( in @ X328 @ ( cartprod @ X326 @ X327 ) ) )
& ( ( X328
= ( kpair @ ( esk1_3 @ X326 @ X327 @ X328 ) @ ( esk2_3 @ X326 @ X327 @ X328 ) ) )
| ~ ( in @ X328 @ ( cartprod @ X326 @ X327 ) ) )
& ( ~ ( in @ X333 @ ( cartprod @ X331 @ X332 ) )
| ( iskpair @ X333 ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk5_2 @ X334 @ X335 ) @ ( dsetconstr @ X334 @ X335 ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( in @ ( esk3_2 @ X334 @ X335 ) @ X334 ) )
& ( ( ( dsetconstr @ X334 @ X335 )
= ( setadjoin @ ( esk5_2 @ X334 @ X335 ) @ emptyset ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( in @ ( esk3_2 @ X334 @ X335 ) @ X334 ) )
& ( ( in @ ( esk5_2 @ X334 @ X335 ) @ ( dsetconstr @ X334 @ X335 ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( in @ ( esk4_2 @ X334 @ X335 ) @ X334 ) )
& ( ( ( dsetconstr @ X334 @ X335 )
= ( setadjoin @ ( esk5_2 @ X334 @ X335 ) @ emptyset ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( in @ ( esk4_2 @ X334 @ X335 ) @ X334 ) )
& ( ( in @ ( esk5_2 @ X334 @ X335 ) @ ( dsetconstr @ X334 @ X335 ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( X335 @ ( esk3_2 @ X334 @ X335 ) ) )
& ( ( ( dsetconstr @ X334 @ X335 )
= ( setadjoin @ ( esk5_2 @ X334 @ X335 ) @ emptyset ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( X335 @ ( esk3_2 @ X334 @ X335 ) ) )
& ( ( in @ ( esk5_2 @ X334 @ X335 ) @ ( dsetconstr @ X334 @ X335 ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( X335 @ ( esk4_2 @ X334 @ X335 ) ) )
& ( ( ( dsetconstr @ X334 @ X335 )
= ( setadjoin @ ( esk5_2 @ X334 @ X335 ) @ emptyset ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( X335 @ ( esk4_2 @ X334 @ X335 ) ) )
& ( ( in @ ( esk5_2 @ X334 @ X335 ) @ ( dsetconstr @ X334 @ X335 ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( ( esk3_2 @ X334 @ X335 )
!= ( esk4_2 @ X334 @ X335 ) ) )
& ( ( ( dsetconstr @ X334 @ X335 )
= ( setadjoin @ ( esk5_2 @ X334 @ X335 ) @ emptyset ) )
| ~ ( in @ X338 @ X334 )
| ~ ( X335 @ X338 )
| ( ( esk3_2 @ X334 @ X335 )
!= ( esk4_2 @ X334 @ X335 ) ) )
& ( ( in @ ( esk6_2 @ X340 @ X341 ) @ X340 )
| ~ ( in @ X342 @ ( dsetconstr @ X340 @ X341 ) )
| ( ( dsetconstr @ X340 @ X341 )
!= ( setadjoin @ X342 @ emptyset ) ) )
& ( ( X341 @ ( esk6_2 @ X340 @ X341 ) )
| ~ ( in @ X342 @ ( dsetconstr @ X340 @ X341 ) )
| ( ( dsetconstr @ X340 @ X341 )
!= ( setadjoin @ X342 @ emptyset ) ) )
& ( ( in @ ( esk8_3 @ X344 @ X345 @ X346 ) @ ( dsetconstr @ X344 @ X345 ) )
| ( in @ ( esk7_3 @ X344 @ X345 @ X346 ) @ X344 )
| ~ ( X345 @ X346 )
| ~ ( in @ X346 @ X344 ) )
& ( ( ( dsetconstr @ X344 @ X345 )
= ( setadjoin @ ( esk8_3 @ X344 @ X345 @ X346 ) @ emptyset ) )
| ( in @ ( esk7_3 @ X344 @ X345 @ X346 ) @ X344 )
| ~ ( X345 @ X346 )
| ~ ( in @ X346 @ X344 ) )
& ( ( in @ ( esk8_3 @ X344 @ X345 @ X346 ) @ ( dsetconstr @ X344 @ X345 ) )
| ( X345 @ ( esk7_3 @ X344 @ X345 @ X346 ) )
| ~ ( X345 @ X346 )
| ~ ( in @ X346 @ X344 ) )
& ( ( ( dsetconstr @ X344 @ X345 )
= ( setadjoin @ ( esk8_3 @ X344 @ X345 @ X346 ) @ emptyset ) )
| ( X345 @ ( esk7_3 @ X344 @ X345 @ X346 ) )
| ~ ( X345 @ X346 )
| ~ ( in @ X346 @ X344 ) )
& ( ( in @ ( esk8_3 @ X344 @ X345 @ X346 ) @ ( dsetconstr @ X344 @ X345 ) )
| ( ( esk7_3 @ X344 @ X345 @ X346 )
!= X346 )
| ~ ( X345 @ X346 )
| ~ ( in @ X346 @ X344 ) )
& ( ( ( dsetconstr @ X344 @ X345 )
= ( setadjoin @ ( esk8_3 @ X344 @ X345 @ X346 ) @ emptyset ) )
| ( ( esk7_3 @ X344 @ X345 @ X346 )
!= X346 )
| ~ ( X345 @ X346 )
| ~ ( in @ X346 @ X344 ) )
& ( ( in @ ( esk11_2 @ X349 @ X350 ) @ ( dsetconstr @ X349 @ X350 ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( in @ ( esk9_2 @ X349 @ X350 ) @ X349 ) )
& ( ( ( dsetconstr @ X349 @ X350 )
= ( setadjoin @ ( esk11_2 @ X349 @ X350 ) @ emptyset ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( in @ ( esk9_2 @ X349 @ X350 ) @ X349 ) )
& ( ( in @ ( esk11_2 @ X349 @ X350 ) @ ( dsetconstr @ X349 @ X350 ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( in @ ( esk10_2 @ X349 @ X350 ) @ X349 ) )
& ( ( ( dsetconstr @ X349 @ X350 )
= ( setadjoin @ ( esk11_2 @ X349 @ X350 ) @ emptyset ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( in @ ( esk10_2 @ X349 @ X350 ) @ X349 ) )
& ( ( in @ ( esk11_2 @ X349 @ X350 ) @ ( dsetconstr @ X349 @ X350 ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( X350 @ ( esk9_2 @ X349 @ X350 ) ) )
& ( ( ( dsetconstr @ X349 @ X350 )
= ( setadjoin @ ( esk11_2 @ X349 @ X350 ) @ emptyset ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( X350 @ ( esk9_2 @ X349 @ X350 ) ) )
& ( ( in @ ( esk11_2 @ X349 @ X350 ) @ ( dsetconstr @ X349 @ X350 ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( X350 @ ( esk10_2 @ X349 @ X350 ) ) )
& ( ( ( dsetconstr @ X349 @ X350 )
= ( setadjoin @ ( esk11_2 @ X349 @ X350 ) @ emptyset ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( X350 @ ( esk10_2 @ X349 @ X350 ) ) )
& ( ( in @ ( esk11_2 @ X349 @ X350 ) @ ( dsetconstr @ X349 @ X350 ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( ( esk9_2 @ X349 @ X350 )
!= ( esk10_2 @ X349 @ X350 ) ) )
& ( ( ( dsetconstr @ X349 @ X350 )
= ( setadjoin @ ( esk11_2 @ X349 @ X350 ) @ emptyset ) )
| ~ ( in @ X353 @ X349 )
| ~ ( X350 @ X353 )
| ( ( esk9_2 @ X349 @ X350 )
!= ( esk10_2 @ X349 @ X350 ) ) )
& singletonsuniq
& setukpairinjL1
& ( ( in @ ( esk12_1 @ X355 )
@ ( dsetconstr @ ( setunion @ X355 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X355 ) ) )
| ~ ( iskpair @ X355 ) )
& ( ( ( dsetconstr @ ( setunion @ X355 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X355 ) )
= ( setadjoin @ ( esk12_1 @ X355 ) @ emptyset ) )
| ~ ( iskpair @ X355 ) )
& ( ~ ( in @ X358 @ X357 )
| ( X357
!= ( setadjoin @ X358 @ emptyset ) )
| ( in @ ( setunion @ X357 ) @ X357 ) )
& ( ( kfst @ ( kpair @ X359 @ X360 ) )
= X359 )
& ( ~ ( in @ X363 @ ( cartprod @ X361 @ X362 ) )
| ( in @ ( kfst @ X363 ) @ X361 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ( in @ ( esk13_1 @ X364 )
@ ( dsetconstr @ ( setunion @ X364 )
@ ^ [Z0: $i] :
( X364
= ( kpair @ ( kfst @ X364 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X364 ) )
& ( ( ( dsetconstr @ ( setunion @ X364 )
@ ^ [Z0: $i] :
( X364
= ( kpair @ ( kfst @ X364 ) @ Z0 ) ) )
= ( setadjoin @ ( esk13_1 @ X364 ) @ emptyset ) )
| ~ ( iskpair @ X364 ) )
& ( ( ksnd @ ( kpair @ X366 @ X367 ) )
= X367 )
& ( ~ ( iskpair @ X368 )
| ( ( kpair @ ( kfst @ X368 ) @ ( ksnd @ X368 ) )
= X368 ) )
& ( ~ ( in @ X371 @ ( cartprod @ X369 @ X370 ) )
| ( in @ ( ksnd @ X371 ) @ X370 ) )
& ( ~ ( in @ ( kpair @ X374 @ X375 ) @ ( cartprod @ X372 @ X373 ) )
| ( in @ X374 @ X372 ) )
& ( ~ ( in @ ( kpair @ X378 @ X379 ) @ ( cartprod @ X376 @ X377 ) )
| ( in @ X379 @ X377 ) )
& cartprodmempaircEq
& ( ~ ( in @ X382 @ X380 )
| ~ ( in @ X383 @ X381 )
| ( ( kfst @ ( kpair @ X382 @ X383 ) )
= X382 ) )
& ( ~ ( in @ X386 @ X384 )
| ~ ( in @ X387 @ X385 )
| ( ( ksnd @ ( kpair @ X386 @ X387 ) )
= X387 ) )
& ( ~ ( in @ X390 @ ( cartprod @ X388 @ X389 ) )
| ( ( kpair @ ( kfst @ X390 ) @ ( ksnd @ X390 ) )
= X390 ) )
& ( ~ ( in @ X394 @ X391 )
| ~ ( in @ X395 @ X392 )
| ~ ( X393 @ X394 @ X395 )
| ( in @ ( kpair @ X394 @ X395 ) @ ( dpsetconstr @ X391 @ X392 @ X393 ) ) )
& ( subset @ ( dpsetconstr @ X396 @ X397 @ X398 ) @ ( cartprod @ X396 @ X397 ) )
& ( subset @ ( dpsetconstr @ X399 @ X400 @ X401 ) @ ( cartprod @ X399 @ X400 ) )
& ( ~ ( in @ X405 @ X402 )
| ~ ( in @ X406 @ X403 )
| ~ ( in @ ( kpair @ X405 @ X406 ) @ ( dpsetconstr @ X402 @ X403 @ X404 ) )
| ( X404 @ X405 @ X406 ) )
& ( ~ ( in @ ( kpair @ X410 @ X411 ) @ ( dpsetconstr @ X407 @ X408 @ X409 ) )
| ( in @ X410 @ X407 ) )
& ( ~ ( in @ ( kpair @ X415 @ X416 ) @ ( dpsetconstr @ X412 @ X413 @ X414 ) )
| ( in @ X416 @ X413 ) )
& ( ~ ( in @ ( kpair @ X420 @ X421 ) @ ( dpsetconstr @ X417 @ X418 @ X419 ) )
| ( X419 @ X420 @ X421 ) )
& ( ( in @ ( esk15_4 @ X422 @ X423 @ X424 @ X427 )
@ ( dsetconstr @ X423
@ ^ [Z0: $i] : ( in @ ( kpair @ X427 @ Z0 ) @ X424 ) ) )
| ~ ( in @ X427 @ X422 )
| ( in @ ( esk14_3 @ X422 @ X423 @ X424 ) @ X422 )
| ~ ( subset @ X424 @ ( cartprod @ X422 @ X423 ) ) )
& ( ( ( dsetconstr @ X423
@ ^ [Z0: $i] : ( in @ ( kpair @ X427 @ Z0 ) @ X424 ) )
= ( setadjoin @ ( esk15_4 @ X422 @ X423 @ X424 @ X427 ) @ emptyset ) )
| ~ ( in @ X427 @ X422 )
| ( in @ ( esk14_3 @ X422 @ X423 @ X424 ) @ X422 )
| ~ ( subset @ X424 @ ( cartprod @ X422 @ X423 ) ) )
& ( ( in @ ( esk15_4 @ X422 @ X423 @ X424 @ X427 )
@ ( dsetconstr @ X423
@ ^ [Z0: $i] : ( in @ ( kpair @ X427 @ Z0 ) @ X424 ) ) )
| ~ ( in @ X427 @ X422 )
| ~ ( in @ X426
@ ( dsetconstr @ X423
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X422 @ X423 @ X424 ) @ Z0 ) @ X424 ) ) )
| ( ( dsetconstr @ X423
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X422 @ X423 @ X424 ) @ Z0 ) @ X424 ) )
!= ( setadjoin @ X426 @ emptyset ) )
| ~ ( subset @ X424 @ ( cartprod @ X422 @ X423 ) ) )
& ( ( ( dsetconstr @ X423
@ ^ [Z0: $i] : ( in @ ( kpair @ X427 @ Z0 ) @ X424 ) )
= ( setadjoin @ ( esk15_4 @ X422 @ X423 @ X424 @ X427 ) @ emptyset ) )
| ~ ( in @ X427 @ X422 )
| ~ ( in @ X426
@ ( dsetconstr @ X423
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X422 @ X423 @ X424 ) @ Z0 ) @ X424 ) ) )
| ( ( dsetconstr @ X423
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X422 @ X423 @ X424 ) @ Z0 ) @ X424 ) )
!= ( setadjoin @ X426 @ emptyset ) )
| ~ ( subset @ X424 @ ( cartprod @ X422 @ X423 ) ) )
& ( ( in @ ( esk16_3 @ X429 @ X430 @ X431 ) @ X429 )
| ~ ( subset @ X431 @ ( cartprod @ X429 @ X430 ) )
| ~ ( in @ X434 @ X429 )
| ( in
@ ( setunion
@ ( dsetconstr @ X430
@ ^ [Z0: $i] : ( in @ ( kpair @ X434 @ Z0 ) @ X431 ) ) )
@ X430 ) )
& ( ~ ( in @ X433
@ ( dsetconstr @ X430
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk16_3 @ X429 @ X430 @ X431 ) @ Z0 ) @ X431 ) ) )
| ( ( dsetconstr @ X430
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk16_3 @ X429 @ X430 @ X431 ) @ Z0 ) @ X431 ) )
!= ( setadjoin @ X433 @ emptyset ) )
| ~ ( subset @ X431 @ ( cartprod @ X429 @ X430 ) )
| ~ ( in @ X434 @ X429 )
| ( in
@ ( setunion
@ ( dsetconstr @ X430
@ ^ [Z0: $i] : ( in @ ( kpair @ X434 @ Z0 ) @ X431 ) ) )
@ X430 ) )
& ( ( in @ ( esk17_3 @ X435 @ X436 @ X437 ) @ X435 )
| ~ ( subset @ X437 @ ( cartprod @ X435 @ X436 ) )
| ~ ( in @ X440 @ X435 )
| ( in @ ( ap @ X435 @ X436 @ X437 @ X440 ) @ X436 ) )
& ( ~ ( in @ X439
@ ( dsetconstr @ X436
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk17_3 @ X435 @ X436 @ X437 ) @ Z0 ) @ X437 ) ) )
| ( ( dsetconstr @ X436
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk17_3 @ X435 @ X436 @ X437 ) @ Z0 ) @ X437 ) )
!= ( setadjoin @ X439 @ emptyset ) )
| ~ ( subset @ X437 @ ( cartprod @ X435 @ X436 ) )
| ~ ( in @ X440 @ X435 )
| ( in @ ( ap @ X435 @ X436 @ X437 @ X440 ) @ X436 ) )
& ( ( subset @ X443 @ ( cartprod @ X441 @ X442 ) )
| ~ ( in @ X443 @ ( funcSet @ X441 @ X442 ) ) )
& ( ( in @ ( esk18_4 @ X441 @ X442 @ X443 @ X444 )
@ ( dsetconstr @ X442
@ ^ [Z0: $i] : ( in @ ( kpair @ X444 @ Z0 ) @ X443 ) ) )
| ~ ( in @ X444 @ X441 )
| ~ ( in @ X443 @ ( funcSet @ X441 @ X442 ) ) )
& ( ( ( dsetconstr @ X442
@ ^ [Z0: $i] : ( in @ ( kpair @ X444 @ Z0 ) @ X443 ) )
= ( setadjoin @ ( esk18_4 @ X441 @ X442 @ X443 @ X444 ) @ emptyset ) )
| ~ ( in @ X444 @ X441 )
| ~ ( in @ X443 @ ( funcSet @ X441 @ X442 ) ) )
& ( ~ ( in @ X448 @ ( funcSet @ X446 @ X447 ) )
| ~ ( in @ X449 @ X446 )
| ( in @ ( ap @ X446 @ X447 @ X448 @ X449 ) @ X447 ) )
& ( ( in @ ( esk19_3 @ X450 @ X451 @ X452 ) @ X450 )
| ~ ( subset @ X452 @ ( cartprod @ X450 @ X451 ) )
| ( in @ X452 @ ( funcSet @ X450 @ X451 ) ) )
& ( ~ ( in @ X454
@ ( dsetconstr @ X451
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk19_3 @ X450 @ X451 @ X452 ) @ Z0 ) @ X452 ) ) )
| ( ( dsetconstr @ X451
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk19_3 @ X450 @ X451 @ X452 ) @ Z0 ) @ X452 ) )
!= ( setadjoin @ X454 @ emptyset ) )
| ~ ( subset @ X452 @ ( cartprod @ X450 @ X451 ) )
| ( in @ X452 @ ( funcSet @ X450 @ X451 ) ) )
& ( ~ ( in @ X458 @ esk20_0 )
| ( in @ ( esk22_0 @ X458 ) @ esk21_0 ) )
& ( ( in @ esk23_0 @ esk20_0 )
| ~ ( subset
@ ( dpsetconstr @ esk20_0 @ esk21_0
@ ^ [Z0: $i] : ( $eq @ ( esk22_0 @ Z0 ) ) )
@ ( cartprod @ esk20_0 @ esk21_0 ) ) )
& ( ~ ( in @ X460
@ ( dsetconstr @ esk21_0
@ ^ [Z0: $i] :
( in @ ( kpair @ esk23_0 @ Z0 )
@ ( dpsetconstr @ esk20_0 @ esk21_0
@ ^ [Z1: $i] : ( $eq @ ( esk22_0 @ Z1 ) ) ) ) ) )
| ( ( dsetconstr @ esk21_0
@ ^ [Z0: $i] :
( in @ ( kpair @ esk23_0 @ Z0 )
@ ( dpsetconstr @ esk20_0 @ esk21_0
@ ^ [Z1: $i] : ( $eq @ ( esk22_0 @ Z1 ) ) ) ) )
!= ( setadjoin @ X460 @ emptyset ) )
| ~ ( subset
@ ( dpsetconstr @ esk20_0 @ esk21_0
@ ^ [Z0: $i] : ( $eq @ ( esk22_0 @ Z0 ) ) )
@ ( cartprod @ esk20_0 @ esk21_0 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])])])]) ).
thf(c_0_76,plain,
! [X465: $i] :
( ( epred1_0 @ X465 )
= ( $eq @ ( esk22_0 @ X465 ) ) ),
introduced(definition) ).
thf(c_0_77,negated_conjecture,
( ( in @ esk23_0 @ esk20_0 )
| ( ( subset @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) @ ( cartprod @ esk20_0 @ esk21_0 ) )
!= $true ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_75]),c_0_76]) ).
thf(c_0_78,plain,
! [X506: $i] :
( ( epred1_0 @ X506 )
= ( $eq @ ( esk22_0 @ X506 ) ) ),
inference(variable_rename,[status(thm)],]) ).
thf(c_0_79,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk5_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( X1 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_80,negated_conjecture,
! [X2: $i] :
( ( in @ ( esk22_0 @ X2 ) @ esk21_0 )
| ~ ( in @ X2 @ esk20_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_81,negated_conjecture,
( ( in @ esk23_0 @ esk20_0 )
| ~ ( subset @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) @ ( cartprod @ esk20_0 @ esk21_0 ) ) ),
inference(cn,[status(thm)],[c_0_77]) ).
thf(c_0_82,negated_conjecture,
! [X2: $i,X6: $i > $i > $o,X3: $i] : ( subset @ ( dpsetconstr @ X2 @ X3 @ X6 ) @ ( cartprod @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_83,plain,
! [X2: $i] :
( ( epred1_0 @ X2 )
= ( $eq @ ( esk22_0 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
thf(c_0_84,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk5_2 @ X2 @ X1 ) @ emptyset ) )
| ( X1 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_85,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( in @ ( esk5_2 @ esk21_0 @ X1 ) @ ( dsetconstr @ esk21_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk21_0 @ X1 ) )
| ~ ( in @ X2 @ esk20_0 )
| ~ ( X1 @ ( esk22_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_86,negated_conjecture,
in @ esk23_0 @ esk20_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
thf(c_0_87,plain,
! [X2: $i,X507: $i] :
( ( ( esk22_0 @ X2 )
= X507 )
<=> ( epred1_0 @ X2 @ X507 ) ),
inference(arg_cong,[status(thm)],[c_0_83]) ).
thf(c_0_88,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk21_0 @ X1 ) )
| ~ ( in @ X2 @ esk20_0 )
| ~ ( X1 @ ( esk22_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_84,c_0_80]) ).
thf(c_0_89,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk21_0 @ X1 ) @ ( dsetconstr @ esk21_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk21_0 @ X1 ) )
| ~ ( X1 @ ( esk22_0 @ esk23_0 ) ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_90,plain,
! [X2: $i] : ( epred1_0 @ X2 @ ( esk22_0 @ X2 ) ),
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_87])]) ).
thf(c_0_91,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk21_0 @ X1 ) )
| ~ ( X1 @ ( esk22_0 @ esk23_0 ) ) ),
inference(spm,[status(thm)],[c_0_88,c_0_86]) ).
thf(c_0_92,plain,
! [X2: $i,X3: $i] :
( ( ( esk22_0 @ X2 )
= X3 )
| ~ ( epred1_0 @ X2 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_87]) ).
thf(c_0_93,plain,
( ( in @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( epred1_0 @ esk23_0 @ ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_94,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ emptyset )
= ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( epred1_0 @ esk23_0 @ ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_91,c_0_90]) ).
thf(c_0_95,plain,
( ( ( esk22_0 @ esk23_0 )
= ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( in @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
thf(c_0_96,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk5_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( X1 @ ( esk4_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_97,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( in @ ( esk5_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 )
| ( ( esk3_2 @ X2 @ X1 )
!= ( esk4_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_98,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ emptyset )
= ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( ( esk22_0 @ esk23_0 )
= ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_94]) ).
thf(c_0_99,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk5_2 @ X2 @ X1 ) @ emptyset ) )
| ( X1 @ ( esk4_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_100,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk5_2 @ X2 @ X1 ) @ emptyset ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 )
| ( ( esk3_2 @ X2 @ X1 )
!= ( esk4_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_101,plain,
( ( ( $eq @ ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
= ( epred1_0 @ esk23_0 ) )
| ( in @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_83,c_0_95]) ).
thf(c_0_102,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( in @ ( esk5_2 @ esk21_0 @ X1 ) @ ( dsetconstr @ esk21_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk21_0 @ X1 ) )
| ~ ( in @ X2 @ esk20_0 )
| ~ ( X1 @ ( esk22_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_96,c_0_80]) ).
thf(c_0_103,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( in @ ( esk5_2 @ esk21_0 @ X1 ) @ ( dsetconstr @ esk21_0 @ X1 ) )
| ( ( esk4_2 @ esk21_0 @ X1 )
!= ( esk3_2 @ esk21_0 @ X1 ) )
| ~ ( in @ X2 @ esk20_0 )
| ~ ( X1 @ ( esk22_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_97,c_0_80]) ).
thf(c_0_104,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ emptyset )
= ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( ( $eq @ ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
= ( epred1_0 @ esk23_0 ) ) ),
inference(spm,[status(thm)],[c_0_83,c_0_98]) ).
thf(c_0_105,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk21_0 @ X1 ) )
| ~ ( in @ X2 @ esk20_0 )
| ~ ( X1 @ ( esk22_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_99,c_0_80]) ).
thf(c_0_106,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ X1 ) )
| ( ( esk4_2 @ esk21_0 @ X1 )
!= ( esk3_2 @ esk21_0 @ X1 ) )
| ~ ( in @ X2 @ esk20_0 )
| ~ ( X1 @ ( esk22_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_100,c_0_80]) ).
thf(c_0_107,plain,
! [X551: $i] :
( ( ( epred1_0 @ esk23_0 @ X551 )
<=> ( ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) )
= X551 ) )
| ( in @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(arg_cong,[status(thm)],[c_0_101]) ).
thf(c_0_108,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk21_0 @ X1 ) @ ( dsetconstr @ esk21_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk21_0 @ X1 ) )
| ~ ( X1 @ ( esk22_0 @ esk23_0 ) ) ),
inference(spm,[status(thm)],[c_0_102,c_0_86]) ).
thf(c_0_109,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk21_0 @ X1 ) @ ( dsetconstr @ esk21_0 @ X1 ) )
| ( ( esk4_2 @ esk21_0 @ X1 )
!= ( esk3_2 @ esk21_0 @ X1 ) )
| ~ ( X1 @ ( esk22_0 @ esk23_0 ) ) ),
inference(spm,[status(thm)],[c_0_103,c_0_86]) ).
thf(c_0_110,plain,
! [X523: $i] :
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ emptyset )
= ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( ( epred1_0 @ esk23_0 @ X523 )
<=> ( ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) )
= X523 ) ) ),
inference(arg_cong,[status(thm)],[c_0_104]) ).
thf(c_0_111,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk21_0 @ X1 ) )
| ~ ( X1 @ ( esk22_0 @ esk23_0 ) ) ),
inference(spm,[status(thm)],[c_0_105,c_0_86]) ).
thf(c_0_112,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ X1 ) )
| ( ( esk4_2 @ esk21_0 @ X1 )
!= ( esk3_2 @ esk21_0 @ X1 ) )
| ~ ( X1 @ ( esk22_0 @ esk23_0 ) ) ),
inference(spm,[status(thm)],[c_0_106,c_0_86]) ).
thf(c_0_113,plain,
! [X2: $i] :
( ( ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) )
= X2 )
| ( in @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ~ ( epred1_0 @ esk23_0 @ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_107]) ).
thf(c_0_114,plain,
( ( in @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( epred1_0 @ esk23_0 @ ( esk4_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_108,c_0_90]) ).
thf(c_0_115,plain,
( ( in @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( ( esk4_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) )
!= ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_109,c_0_90]) ).
thf(c_0_116,plain,
! [X2: $i] :
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ emptyset )
= ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) )
= X2 )
| ~ ( epred1_0 @ esk23_0 @ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_110]) ).
thf(c_0_117,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ emptyset )
= ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( epred1_0 @ esk23_0 @ ( esk4_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_90]) ).
thf(c_0_118,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ emptyset )
= ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) )
| ( ( esk4_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) )
!= ( esk3_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_112,c_0_90]) ).
thf(c_0_119,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( X1 @ ( esk6_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
| ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_120,plain,
in @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115]) ).
thf(c_0_121,plain,
( ( setadjoin @ ( esk5_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ emptyset )
= ( dsetconstr @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]) ).
thf(c_0_122,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk6_2 @ X2 @ X1 ) @ X2 )
| ~ ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
| ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_123,negated_conjecture,
epred1_0 @ esk23_0 @ ( esk6_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121])]) ).
thf(c_0_124,plain,
! [X505: $i] :
( ( ~ ( epred2_0 @ X505 )
| ( in @ ( kpair @ esk23_0 @ X505 ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) ) )
& ( ~ ( in @ ( kpair @ esk23_0 @ X505 ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) )
| ( epred2_0 @ X505 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_125,negated_conjecture,
! [X3: $i,X2: $i,X6: $i > $i > $o,X5: $i,X4: $i] :
( ( in @ ( kpair @ X2 @ X4 ) @ ( dpsetconstr @ X3 @ X5 @ X6 ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X5 )
| ~ ( X6 @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_126,negated_conjecture,
in @ ( esk6_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) ) @ esk21_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_120]),c_0_121])]) ).
thf(c_0_127,plain,
( ( esk6_2 @ esk21_0 @ ( epred1_0 @ esk23_0 ) )
= ( esk22_0 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_92,c_0_123]) ).
thf(c_0_128,plain,
! [X2: $i] :
( ( epred2_0 @ X2 )
| ~ ( in @ ( kpair @ esk23_0 @ X2 ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
thf(c_0_129,plain,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ ( esk22_0 @ X2 ) ) @ ( dpsetconstr @ X3 @ X4 @ epred1_0 ) )
| ~ ( in @ ( esk22_0 @ X2 ) @ X4 )
| ~ ( in @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_125,c_0_90]) ).
thf(c_0_130,negated_conjecture,
in @ ( esk22_0 @ esk23_0 ) @ esk21_0,
inference(rw,[status(thm)],[c_0_126,c_0_127]) ).
thf(c_0_131,plain,
epred2_0 @ ( esk22_0 @ esk23_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]),c_0_86])]) ).
thf(c_0_132,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i > $i > $o] :
( ( X6 @ X2 @ X3 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ X4 @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_133,negated_conjecture,
! [X2: $i] :
( ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 )
| ~ ( iskpair @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_134,plain,
! [X2: $i] :
( ( in @ ( kpair @ esk23_0 @ X2 ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
thf(c_0_135,negated_conjecture,
( ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk3_2 @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_89,c_0_131]) ).
thf(c_0_136,negated_conjecture,
( ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk4_2 @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_108,c_0_131]) ).
thf(c_0_137,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk4_2 @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_131]) ).
thf(c_0_138,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk3_2 @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_91,c_0_131]) ).
thf(c_0_139,plain,
! [X466: $i] :
( ( epred2_0 @ X466 )
<=> ( in @ ( kpair @ esk23_0 @ X466 ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) ) ),
introduced(definition) ).
thf(c_0_140,negated_conjecture,
! [X3: $i,X6: $i > $i > $o,X4: $i,X2: $i] :
( ( X6 @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
| ~ ( in @ X2 @ ( dpsetconstr @ X3 @ X4 @ X6 ) )
| ~ ( iskpair @ X2 ) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
thf(c_0_141,plain,
( ( in @ ( kpair @ esk23_0 @ ( esk3_2 @ esk21_0 @ epred2_0 ) ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) )
| ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
thf(c_0_142,negated_conjecture,
! [X3: $i,X2: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_143,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_144,negated_conjecture,
! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_145,plain,
( ( in @ ( kpair @ esk23_0 @ ( esk4_2 @ esk21_0 @ epred2_0 ) ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) )
| ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_134,c_0_136]) ).
thf(c_0_146,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( in @ ( kpair @ esk23_0 @ ( esk4_2 @ esk21_0 @ epred2_0 ) ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_134,c_0_137]) ).
thf(c_0_147,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( in @ ( kpair @ esk23_0 @ ( esk3_2 @ esk21_0 @ epred2_0 ) ) @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_134,c_0_138]) ).
thf(c_0_148,negated_conjecture,
! [X2: $i] :
( ( ( in @ X2 @ ( dsetconstr @ esk21_0 @ epred2_0 ) )
!= $true )
| ( ( dsetconstr @ esk21_0 @ epred2_0 )
!= ( setadjoin @ X2 @ emptyset ) )
| ( ( subset @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) @ ( cartprod @ esk20_0 @ esk21_0 ) )
!= $true ) ),
inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_75]),c_0_76]),c_0_139]),c_0_76]),c_0_139]),c_0_76]) ).
thf(c_0_149,negated_conjecture,
( ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( epred1_0 @ esk23_0 @ ( esk3_2 @ esk21_0 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]),c_0_143]),c_0_144])]) ).
thf(c_0_150,negated_conjecture,
( ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( epred1_0 @ esk23_0 @ ( esk4_2 @ esk21_0 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_145]),c_0_142]),c_0_143]),c_0_144])]) ).
thf(c_0_151,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( epred1_0 @ esk23_0 @ ( esk4_2 @ esk21_0 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_146]),c_0_142]),c_0_143]),c_0_144])]) ).
thf(c_0_152,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( epred1_0 @ esk23_0 @ ( esk3_2 @ esk21_0 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_147]),c_0_142]),c_0_143]),c_0_144])]) ).
thf(c_0_153,negated_conjecture,
! [X2: $i] :
( ( ( dsetconstr @ esk21_0 @ epred2_0 )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( subset @ ( dpsetconstr @ esk20_0 @ esk21_0 @ epred1_0 ) @ ( cartprod @ esk20_0 @ esk21_0 ) )
| ~ ( in @ X2 @ ( dsetconstr @ esk21_0 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[c_0_148]) ).
thf(c_0_154,plain,
( ( ( esk22_0 @ esk23_0 )
= ( esk3_2 @ esk21_0 @ epred2_0 ) )
| ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_149]) ).
thf(c_0_155,plain,
( ( ( esk22_0 @ esk23_0 )
= ( esk4_2 @ esk21_0 @ epred2_0 ) )
| ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_150]) ).
thf(c_0_156,negated_conjecture,
( ( in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( ( esk4_2 @ esk21_0 @ epred2_0 )
!= ( esk3_2 @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_109,c_0_131]) ).
thf(c_0_157,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( ( esk22_0 @ esk23_0 )
= ( esk4_2 @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_151]) ).
thf(c_0_158,plain,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( ( esk22_0 @ esk23_0 )
= ( esk3_2 @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_152]) ).
thf(c_0_159,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) )
| ( ( esk4_2 @ esk21_0 @ epred2_0 )
!= ( esk3_2 @ esk21_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_112,c_0_131]) ).
thf(c_0_160,negated_conjecture,
! [X2: $i] :
( ( ( dsetconstr @ esk21_0 @ epred2_0 )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ ( dsetconstr @ esk21_0 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_82])]) ).
thf(c_0_161,plain,
in @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ ( dsetconstr @ esk21_0 @ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_156]) ).
thf(c_0_162,plain,
( ( setadjoin @ ( esk5_2 @ esk21_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk21_0 @ epred2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_159]) ).
thf(c_0_163,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_162])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU678^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:09:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.49 Running higher-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.53/1.01 # Version: 3.1.0-ho
% 3.53/1.01 # Preprocessing class: HSLMSLSSLLLCHSA.
% 3.53/1.01 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.53/1.01 # Starting ho_unfolding_5 with 1200s (4) cores
% 3.53/1.01 # Starting pre_casc_3 with 300s (1) cores
% 3.53/1.01 # Starting new_ho_10_cnf2 with 300s (1) cores
% 3.53/1.01 # Starting full_lambda_10 with 300s (1) cores
% 3.53/1.01 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 3.53/1.01 # pre_casc_3 with pid 16756 completed with status 0
% 3.53/1.01 # Result found by pre_casc_3
% 3.53/1.01 # Preprocessing class: HSLMSLSSLLLCHSA.
% 3.53/1.01 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.53/1.01 # Starting ho_unfolding_5 with 1200s (4) cores
% 3.53/1.01 # Starting pre_casc_3 with 300s (1) cores
% 3.53/1.01 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 3.53/1.01 # Search class: HGHSM-FSLM32-MHSMMSBN
% 3.53/1.01 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 3.53/1.01 # Starting full_lambda_5 with 28s (1) cores
% 3.53/1.01 # full_lambda_5 with pid 16770 completed with status 0
% 3.53/1.01 # Result found by full_lambda_5
% 3.53/1.01 # Preprocessing class: HSLMSLSSLLLCHSA.
% 3.53/1.01 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.53/1.01 # Starting ho_unfolding_5 with 1200s (4) cores
% 3.53/1.01 # Starting pre_casc_3 with 300s (1) cores
% 3.53/1.01 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 3.53/1.01 # Search class: HGHSM-FSLM32-MHSMMSBN
% 3.53/1.01 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 3.53/1.01 # Starting full_lambda_5 with 28s (1) cores
% 3.53/1.01 # Preprocessing time : 0.004 s
% 3.53/1.01 # Presaturation interreduction done
% 3.53/1.01
% 3.53/1.01 # Proof found!
% 3.53/1.01 # SZS status Theorem
% 3.53/1.01 # SZS output start CNFRefutation
% See solution above
% 3.53/1.01 # Parsed axioms : 432
% 3.53/1.01 # Removed by relevancy pruning/SinE : 391
% 3.53/1.01 # Initial clauses : 245
% 3.53/1.01 # Removed in clause preprocessing : 0
% 3.53/1.01 # Initial clauses in saturation : 245
% 3.53/1.01 # Processed clauses : 1961
% 3.53/1.01 # ...of these trivial : 20
% 3.53/1.01 # ...subsumed : 498
% 3.53/1.01 # ...remaining for further processing : 1443
% 3.53/1.01 # Other redundant clauses eliminated : 107
% 3.53/1.01 # Clauses deleted for lack of memory : 0
% 3.53/1.01 # Backward-subsumed : 24
% 3.53/1.01 # Backward-rewritten : 125
% 3.53/1.01 # Generated clauses : 14319
% 3.53/1.01 # ...of the previous two non-redundant : 13892
% 3.53/1.01 # ...aggressively subsumed : 0
% 3.53/1.01 # Contextual simplify-reflections : 16
% 3.53/1.01 # Paramodulations : 13864
% 3.53/1.01 # Factorizations : 0
% 3.53/1.01 # NegExts : 110
% 3.53/1.01 # Equation resolutions : 107
% 3.53/1.01 # Disequality decompositions : 0
% 3.53/1.01 # Total rewrite steps : 1221
% 3.53/1.01 # ...of those cached : 1043
% 3.53/1.01 # Propositional unsat checks : 0
% 3.53/1.01 # Propositional check models : 0
% 3.53/1.01 # Propositional check unsatisfiable : 0
% 3.53/1.01 # Propositional clauses : 0
% 3.53/1.01 # Propositional clauses after purity: 0
% 3.53/1.01 # Propositional unsat core size : 0
% 3.53/1.01 # Propositional preprocessing time : 0.000
% 3.53/1.01 # Propositional encoding time : 0.000
% 3.53/1.01 # Propositional solver time : 0.000
% 3.53/1.01 # Success case prop preproc time : 0.000
% 3.53/1.01 # Success case prop encoding time : 0.000
% 3.53/1.01 # Success case prop solver time : 0.000
% 3.53/1.01 # Current number of processed clauses : 984
% 3.53/1.01 # Positive orientable unit clauses : 194
% 3.53/1.01 # Positive unorientable unit clauses: 0
% 3.53/1.01 # Negative unit clauses : 0
% 3.53/1.01 # Non-unit-clauses : 790
% 3.53/1.01 # Current number of unprocessed clauses: 12102
% 3.53/1.01 # ...number of literals in the above : 52829
% 3.53/1.01 # Current number of archived formulas : 0
% 3.53/1.01 # Current number of archived clauses : 458
% 3.53/1.01 # Clause-clause subsumption calls (NU) : 102055
% 3.53/1.01 # Rec. Clause-clause subsumption calls : 59543
% 3.53/1.01 # Non-unit clause-clause subsumptions : 533
% 3.53/1.01 # Unit Clause-clause subsumption calls : 3367
% 3.53/1.01 # Rewrite failures with RHS unbound : 0
% 3.53/1.01 # BW rewrite match attempts : 94
% 3.53/1.01 # BW rewrite match successes : 19
% 3.53/1.01 # Condensation attempts : 0
% 3.53/1.01 # Condensation successes : 0
% 3.53/1.01 # Termbank termtop insertions : 556546
% 3.53/1.01 # Search garbage collected termcells : 8620
% 3.53/1.01
% 3.53/1.01 # -------------------------------------------------
% 3.53/1.01 # User time : 0.466 s
% 3.53/1.01 # System time : 0.025 s
% 3.53/1.01 # Total time : 0.491 s
% 3.53/1.01 # Maximum resident set size: 4768 pages
% 3.53/1.01
% 3.53/1.01 # -------------------------------------------------
% 3.53/1.01 # User time : 0.477 s
% 3.53/1.01 # System time : 0.026 s
% 3.53/1.01 # Total time : 0.504 s
% 3.53/1.01 # Maximum resident set size: 2212 pages
% 3.53/1.01 % E---3.1 exiting
% 3.53/1.01 % E exiting
%------------------------------------------------------------------------------