%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU781^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n008.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 03:30:11 EDT 2024
% Result : Theorem 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 333
% Syntax : Number of formulae : 362 ( 23 unt; 322 typ; 0 def)
% Number of atoms : 1269 ( 32 equ; 0 cnn)
% Maximal formula atoms : 447 ( 31 avg)
% Number of connectives : 2847 ( 118 ~; 147 |; 335 &;1500 @)
% ( 9 <=>; 738 =>; 0 <=; 0 <~>)
% Maximal formula depth : 374 ( 32 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 324 ( 322 usr; 304 con; 0-5 aty)
% Number of variables : 226 ( 18 ^ 205 !; 3 ?; 226 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_30,type,
powersetAx: $o ).
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_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_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_199,type,
singletonprop: $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_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_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_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
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,
lamProp: $o ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
complementSubsetComplementIntersect: $o ).
thf(decl_311,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_312,type,
contraSubsetComplement: $o ).
thf(decl_313,type,
complementTcontraSubset: $o ).
thf(decl_314,type,
binunionTILcontra: $o ).
thf(decl_315,type,
binunionTIRcontra: $o ).
thf(decl_316,type,
inIntersectImpInUnion: $o ).
thf(decl_317,type,
inIntersectImpInUnion2: $o ).
thf(decl_318,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_319,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_320,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_321,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_322,type,
binunionTE: $o ).
thf(decl_323,type,
binunionTEcontra: $o ).
thf(decl_324,type,
demorgan2a1: $o ).
thf(decl_325,type,
complementUnionInPowersetComplement: $o ).
thf(decl_326,type,
demorgan2a2: $o ).
thf(decl_327,type,
demorgan1a: $o ).
thf(decl_328,type,
demorgan1b: $o ).
thf(decl_329,type,
demorgan1: $o ).
thf(decl_330,type,
demorgan2a: $o ).
thf(decl_331,type,
demorgan2b2: $o ).
thf(decl_332,type,
demorgan2b: $o ).
thf(decl_333,type,
demorgan2: $o ).
thf(decl_334,type,
woz13rule0: $o ).
thf(decl_335,type,
woz13rule1: $o ).
thf(decl_336,type,
woz13rule2: $o ).
thf(decl_337,type,
woz13rule3: $o ).
thf(decl_338,type,
woz13rule4: $o ).
thf(decl_339,type,
woz1_1: $o ).
thf(decl_340,type,
woz1_2: $o ).
thf(decl_341,type,
woz1_3: $o ).
thf(decl_342,type,
woz1_4: $o ).
thf(decl_343,type,
woz1_5: $o ).
thf(decl_344,type,
breln1: $i > $i > $o ).
thf(decl_345,type,
breln1all2: $o ).
thf(decl_347,type,
breln1SetBreln1: $o ).
thf(decl_354,type,
choice2fnsingleton: $o ).
thf(decl_355,type,
setOfPairsIsBReln1: $o ).
thf(decl_356,type,
breln1all1: $o ).
thf(decl_357,type,
subbreln1: $o ).
thf(decl_358,type,
eqbreln1: $o ).
thf(decl_360,type,
breln1invprop: $o ).
thf(decl_361,type,
breln1invI: $o ).
thf(decl_362,type,
breln1invE: $o ).
thf(decl_363,type,
breln1compset: $i > $i > $i > $i ).
thf(decl_364,type,
breln1compprop: $o ).
thf(decl_365,type,
breln1compI: $o ).
thf(decl_366,type,
breln1compE: $o ).
thf(decl_367,type,
esk1_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_368,type,
esk2_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_369,type,
esk3_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_370,type,
esk4_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_371,type,
esk5_4: $i > $i > $i > $i > $i ).
thf(decl_372,type,
esk6_4: $i > $i > $i > $i > $i ).
thf(decl_373,type,
esk7_4: $i > $i > $i > $i > $i ).
thf(decl_374,type,
esk8_4: $i > $i > $i > $i > $i ).
thf(decl_375,type,
esk9_4: $i > $i > $i > $i > $i ).
thf(decl_376,type,
esk10_4: $i > $i > $i > $i > $i ).
thf(decl_377,type,
esk11_5: $i > $i > $i > $i > $i > $i ).
thf(decl_378,type,
esk12_0: $i ).
thf(decl_379,type,
esk13_0: $i ).
thf(decl_380,type,
esk14_0: $i ).
thf(decl_381,type,
esk15_0: $i ).
thf(decl_382,type,
esk16_0: $i ).
thf(decl_383,type,
epred1_0: $o ).
thf(breln1,axiom,
( breln1
= ( ^ [X4: $i,X33: $i] : ( breln @ X4 @ X4 @ X33 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
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/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(breln1compprop,axiom,
( breln1compprop
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( breln1 @ X4 @ ( breln1compset @ X4 @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compprop) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1) ).
thf(breln1compE,axiom,
( breln1compE
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) )
=> ? [X14: $i] :
( ( in @ X14 @ X4 )
& ( in @ ( kpair @ X2 @ X14 ) @ X33 )
& ( in @ ( kpair @ X14 @ X3 ) @ X35 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compE) ).
thf(breln1compI,axiom,
( breln1compI
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X14 ) @ X33 )
=> ( ( in @ ( kpair @ X14 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compI) ).
thf(breln1compEex,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
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) )
=> ! [X54: $o] :
( ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X14 ) @ X33 )
=> ( ( in @ ( kpair @ X14 @ X3 ) @ X35 )
=> X54 ) ) )
=> X54 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).
thf(c_0_11,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1]) ).
thf(c_0_12,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_13,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,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_15,axiom,
( breln1compprop
= ( ! [X4: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X4 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X4 ) )
=> ( subset @ ( breln1compset @ X4 @ X33 @ X35 ) @ ( cartprod @ X4 @ X4 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[breln1compprop,c_0_13]) ).
thf(c_0_16,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_12]) ).
thf(c_0_17,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_12]) ).
thf(c_0_18,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_12]) ).
thf(c_0_19,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_12]) ).
thf(c_0_20,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_14,c_0_12]) ).
thf(c_0_21,axiom,
( breln1compE
= ( ! [X4: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X4 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) )
=> ? [X14: $i] :
( ( in @ X14 @ X4 )
& ( in @ ( kpair @ X2 @ X14 ) @ X33 )
& ( in @ ( kpair @ X14 @ X3 ) @ X35 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[breln1compE,c_0_13]) ).
thf(c_0_22,axiom,
( breln1compI
= ( ! [X4: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X4 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X14 ) @ X33 )
=> ( ( in @ ( kpair @ X14 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[breln1compI,c_0_13]) ).
thf(c_0_23,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
=> ( 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
=> ( ! [X108: $i,X109: $i,X110: $i > $i > $o] : ( subset @ ( dpsetconstr @ X108 @ X109 @ X110 ) @ ( cartprod @ X108 @ X109 ) )
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( ! [X111: $i,X112: $i,X113: $i] :
( ( subset @ X113 @ ( cartprod @ X111 @ X112 ) )
=> ! [X114: $i > $o] :
( ! [X115: $i] :
( ( in @ X115 @ X111 )
=> ! [X116: $i] :
( ( in @ X116 @ X112 )
=> ( ( in @ ( kpair @ X115 @ X116 ) @ X113 )
=> ( X114 @ ( kpair @ X115 @ X116 ) ) ) ) )
=> ! [X117: $i] :
( ( in @ X117 @ X113 )
=> ( X114 @ X117 ) ) ) )
=> ( ! [X118: $i,X119: $i,X120: $i] :
( ( subset @ X120 @ ( cartprod @ X118 @ X119 ) )
=> ! [X121: $i > $o] :
( ! [X122: $i] :
( ( in @ X122 @ X118 )
=> ! [X123: $i] :
( ( in @ X123 @ X119 )
=> ( ( in @ ( kpair @ X122 @ X123 ) @ X120 )
=> ( X121 @ ( kpair @ X122 @ X123 ) ) ) ) )
=> ! [X124: $i] :
( ( in @ X124 @ X120 )
=> ( X121 @ X124 ) ) ) )
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( ! [X125: $i,X126: $i,X127: $i] :
( ( subset @ X127 @ ( cartprod @ X125 @ X126 ) )
=> ! [X128: $i] :
( ( subset @ X128 @ ( cartprod @ X125 @ X126 ) )
=> ( ! [X129: $i] :
( ( in @ X129 @ X125 )
=> ! [X130: $i] :
( ( in @ X130 @ X126 )
=> ( ( in @ ( kpair @ X129 @ X130 ) @ X127 )
=> ( in @ ( kpair @ X129 @ X130 ) @ X128 ) ) ) )
=> ( subset @ X127 @ X128 ) ) ) )
=> ( ! [X131: $i,X132: $i,X133: $i] :
( ( subset @ X133 @ ( cartprod @ X131 @ X132 ) )
=> ! [X134: $i] :
( ( subset @ X134 @ ( cartprod @ X131 @ X132 ) )
=> ( ! [X135: $i] :
( ( in @ X135 @ X131 )
=> ! [X136: $i] :
( ( in @ X136 @ X132 )
=> ( ( in @ ( kpair @ X135 @ X136 ) @ X133 )
=> ( in @ ( kpair @ X135 @ X136 ) @ X134 ) ) ) )
=> ( ! [X137: $i] :
( ( in @ X137 @ X131 )
=> ! [X138: $i] :
( ( in @ X138 @ X132 )
=> ( ( in @ ( kpair @ X137 @ X138 ) @ X134 )
=> ( in @ ( kpair @ X137 @ X138 ) @ X133 ) ) ) )
=> ( X133 = X134 ) ) ) ) )
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( ! [X139: $i,X140: $i] :
( ( subset @ X140 @ ( cartprod @ X139 @ X139 ) )
=> ! [X141: $i] :
( ( subset @ X141 @ ( cartprod @ X139 @ X139 ) )
=> ( subset @ ( breln1compset @ X139 @ X140 @ X141 ) @ ( cartprod @ X139 @ X139 ) ) ) )
=> ( ! [X142: $i,X143: $i] :
( ( subset @ X143 @ ( cartprod @ X142 @ X142 ) )
=> ! [X144: $i] :
( ( subset @ X144 @ ( cartprod @ X142 @ X142 ) )
=> ! [X145: $i] :
( ( in @ X145 @ X142 )
=> ! [X146: $i] :
( ( in @ X146 @ X142 )
=> ! [X147: $i] :
( ( in @ X147 @ X142 )
=> ( ( in @ ( kpair @ X145 @ X147 ) @ X143 )
=> ( ( in @ ( kpair @ X147 @ X146 ) @ X144 )
=> ( in @ ( kpair @ X145 @ X146 ) @ ( breln1compset @ X142 @ X143 @ X144 ) ) ) ) ) ) ) ) )
=> ( ! [X148: $i,X149: $i] :
( ( subset @ X149 @ ( cartprod @ X148 @ X148 ) )
=> ! [X150: $i] :
( ( subset @ X150 @ ( cartprod @ X148 @ X148 ) )
=> ! [X151: $i] :
( ( in @ X151 @ X148 )
=> ! [X152: $i] :
( ( in @ X152 @ X148 )
=> ( ( in @ ( kpair @ X151 @ X152 ) @ ( breln1compset @ X148 @ X149 @ X150 ) )
=> ? [X153: $i] :
( ( in @ X153 @ X148 )
& ( in @ ( kpair @ X151 @ X153 ) @ X149 )
& ( in @ ( kpair @ X153 @ X152 ) @ X150 ) ) ) ) ) ) )
=> ! [X4: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X4 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) )
=> ! [X54: $o] :
( ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X14 ) @ X33 )
=> ( ( in @ ( kpair @ X14 @ X3 ) @ X35 )
=> X54 ) ) )
=> X54 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[breln1compEex]),c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_13]),c_0_21]),c_0_22])]) ).
thf(c_0_24,negated_conjecture,
! [X154: $i,X155: $i,X156: $i > $i > $o,X157: $i,X158: $i,X159: $i,X160: $i > $o,X163: $i,X164: $i,X165: $i,X166: $i,X167: $i > $o,X170: $i,X171: $i,X172: $i,X173: $i,X174: $i,X177: $i,X178: $i,X179: $i,X180: $i,X185: $i,X186: $i,X187: $i,X188: $i,X189: $i,X190: $i,X191: $i,X192: $i,X193: $i,X194: $i,X195: $i,X196: $i,X197: $i,X198: $i,X206: $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
& 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
& ( subset @ ( dpsetconstr @ X154 @ X155 @ X156 ) @ ( cartprod @ X154 @ X155 ) )
& dpsetconstrERa
& dpsetconstrEL1
& dpsetconstrEL2
& dpsetconstrER
& funcImageSingleton
& apProp
& app
& infuncsetfunc
& ap2p
& funcinfuncset
& lamProp
& lamp
& lam2p
& ( ( in @ ( esk1_4 @ X157 @ X158 @ X159 @ X160 ) @ X157 )
| ~ ( in @ X163 @ X159 )
| ( X160 @ X163 )
| ~ ( subset @ X159 @ ( cartprod @ X157 @ X158 ) ) )
& ( ( in @ ( esk2_4 @ X157 @ X158 @ X159 @ X160 ) @ X158 )
| ~ ( in @ X163 @ X159 )
| ( X160 @ X163 )
| ~ ( subset @ X159 @ ( cartprod @ X157 @ X158 ) ) )
& ( ( in @ ( kpair @ ( esk1_4 @ X157 @ X158 @ X159 @ X160 ) @ ( esk2_4 @ X157 @ X158 @ X159 @ X160 ) ) @ X159 )
| ~ ( in @ X163 @ X159 )
| ( X160 @ X163 )
| ~ ( subset @ X159 @ ( cartprod @ X157 @ X158 ) ) )
& ( ~ ( X160 @ ( kpair @ ( esk1_4 @ X157 @ X158 @ X159 @ X160 ) @ ( esk2_4 @ X157 @ X158 @ X159 @ X160 ) ) )
| ~ ( in @ X163 @ X159 )
| ( X160 @ X163 )
| ~ ( subset @ X159 @ ( cartprod @ X157 @ X158 ) ) )
& ( ( in @ ( esk3_4 @ X164 @ X165 @ X166 @ X167 ) @ X164 )
| ~ ( in @ X170 @ X166 )
| ( X167 @ X170 )
| ~ ( subset @ X166 @ ( cartprod @ X164 @ X165 ) ) )
& ( ( in @ ( esk4_4 @ X164 @ X165 @ X166 @ X167 ) @ X165 )
| ~ ( in @ X170 @ X166 )
| ( X167 @ X170 )
| ~ ( subset @ X166 @ ( cartprod @ X164 @ X165 ) ) )
& ( ( in @ ( kpair @ ( esk3_4 @ X164 @ X165 @ X166 @ X167 ) @ ( esk4_4 @ X164 @ X165 @ X166 @ X167 ) ) @ X166 )
| ~ ( in @ X170 @ X166 )
| ( X167 @ X170 )
| ~ ( subset @ X166 @ ( cartprod @ X164 @ X165 ) ) )
& ( ~ ( X167 @ ( kpair @ ( esk3_4 @ X164 @ X165 @ X166 @ X167 ) @ ( esk4_4 @ X164 @ X165 @ X166 @ X167 ) ) )
| ~ ( in @ X170 @ X166 )
| ( X167 @ X170 )
| ~ ( subset @ X166 @ ( cartprod @ X164 @ X165 ) ) )
& ex1E2
& funcGraphProp1
& funcGraphProp3
& funcGraphProp2
& funcextLem
& funcGraphProp4
& ( ( in @ ( esk5_4 @ X171 @ X172 @ X173 @ X174 ) @ X171 )
| ( subset @ X173 @ X174 )
| ~ ( subset @ X174 @ ( cartprod @ X171 @ X172 ) )
| ~ ( subset @ X173 @ ( cartprod @ X171 @ X172 ) ) )
& ( ( in @ ( esk6_4 @ X171 @ X172 @ X173 @ X174 ) @ X172 )
| ( subset @ X173 @ X174 )
| ~ ( subset @ X174 @ ( cartprod @ X171 @ X172 ) )
| ~ ( subset @ X173 @ ( cartprod @ X171 @ X172 ) ) )
& ( ( in @ ( kpair @ ( esk5_4 @ X171 @ X172 @ X173 @ X174 ) @ ( esk6_4 @ X171 @ X172 @ X173 @ X174 ) ) @ X173 )
| ( subset @ X173 @ X174 )
| ~ ( subset @ X174 @ ( cartprod @ X171 @ X172 ) )
| ~ ( subset @ X173 @ ( cartprod @ X171 @ X172 ) ) )
& ( ~ ( in @ ( kpair @ ( esk5_4 @ X171 @ X172 @ X173 @ X174 ) @ ( esk6_4 @ X171 @ X172 @ X173 @ X174 ) ) @ X174 )
| ( subset @ X173 @ X174 )
| ~ ( subset @ X174 @ ( cartprod @ X171 @ X172 ) )
| ~ ( subset @ X173 @ ( cartprod @ X171 @ X172 ) ) )
& ( ( in @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ X177 )
| ( X179 = X180 )
| ( in @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ X177 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) @ X178 )
| ( X179 = X180 )
| ( in @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ X177 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( kpair @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X180 )
| ( X179 = X180 )
| ( in @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ X177 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ~ ( in @ ( kpair @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X179 )
| ( X179 = X180 )
| ( in @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ X177 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ X177 )
| ( X179 = X180 )
| ( in @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) @ X178 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) @ X178 )
| ( X179 = X180 )
| ( in @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) @ X178 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( kpair @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X180 )
| ( X179 = X180 )
| ( in @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) @ X178 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ~ ( in @ ( kpair @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X179 )
| ( X179 = X180 )
| ( in @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) @ X178 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ X177 )
| ( X179 = X180 )
| ( in @ ( kpair @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X179 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) @ X178 )
| ( X179 = X180 )
| ( in @ ( kpair @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X179 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( kpair @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X180 )
| ( X179 = X180 )
| ( in @ ( kpair @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X179 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ~ ( in @ ( kpair @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X179 )
| ( X179 = X180 )
| ( in @ ( kpair @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X179 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ X177 )
| ( X179 = X180 )
| ~ ( in @ ( kpair @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X180 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) @ X178 )
| ( X179 = X180 )
| ~ ( in @ ( kpair @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X180 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ( in @ ( kpair @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X180 )
| ( X179 = X180 )
| ~ ( in @ ( kpair @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X180 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& ( ~ ( in @ ( kpair @ ( esk9_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk10_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X179 )
| ( X179 = X180 )
| ~ ( in @ ( kpair @ ( esk7_4 @ X177 @ X178 @ X179 @ X180 ) @ ( esk8_4 @ X177 @ X178 @ X179 @ X180 ) ) @ X180 )
| ~ ( subset @ X180 @ ( cartprod @ X177 @ X178 ) )
| ~ ( subset @ X179 @ ( cartprod @ X177 @ X178 ) ) )
& funcext
& funcext2
& ap2apEq1
& ap2apEq2
& beta1
& eta1
& lam2lamEq
& beta2
& eta2
& iffalseProp1
& iffalseProp2
& iftrueProp1
& iftrueProp2
& ifSingleton
& ifp
& theeq
& iftrue
& iffalse
& iftrueorfalse
& binintersectT_lem
& binunionT_lem
& powersetT_lem
& setminusT_lem
& complementT_lem
& setextT
& subsetTI
& powersetTI1
& powersetTE1
& complementTI1
& complementTE1
& binintersectTELcontra
& binintersectTERcontra
& contrasubsetT
& contrasubsetT1
& contrasubsetT2
& contrasubsetT3
& doubleComplementI1
& doubleComplementE1
& doubleComplementSub1
& doubleComplementSub2
& doubleComplementEq
& complementTnotintersectT
& complementImpComplementIntersect
& complementSubsetComplementIntersect
& complementInPowersetComplementIntersect
& contraSubsetComplement
& complementTcontraSubset
& binunionTILcontra
& binunionTIRcontra
& inIntersectImpInUnion
& inIntersectImpInUnion2
& inIntersectImpInIntersectUnions
& intersectInPowersetIntersectUnions
& inComplementUnionImpNotIn1
& inComplementUnionImpInComplement1
& binunionTE
& binunionTEcontra
& demorgan2a1
& complementUnionInPowersetComplement
& demorgan2a2
& demorgan1a
& demorgan1b
& demorgan1
& demorgan2a
& demorgan2b2
& demorgan2b
& demorgan2
& woz13rule0
& woz13rule1
& woz13rule2
& woz13rule3
& woz13rule4
& woz1_1
& woz1_2
& woz1_3
& woz1_4
& woz1_5
& breln1all2
& breln1SetBreln1
& choice2fnsingleton
& setOfPairsIsBReln1
& breln1all1
& subbreln1
& eqbreln1
& breln1invprop
& breln1invI
& breln1invE
& ( ~ ( subset @ X186 @ ( cartprod @ X185 @ X185 ) )
| ~ ( subset @ X187 @ ( cartprod @ X185 @ X185 ) )
| ( subset @ ( breln1compset @ X185 @ X186 @ X187 ) @ ( cartprod @ X185 @ X185 ) ) )
& ( ~ ( subset @ X189 @ ( cartprod @ X188 @ X188 ) )
| ~ ( subset @ X190 @ ( cartprod @ X188 @ X188 ) )
| ~ ( in @ X191 @ X188 )
| ~ ( in @ X192 @ X188 )
| ~ ( in @ X193 @ X188 )
| ~ ( in @ ( kpair @ X191 @ X193 ) @ X189 )
| ~ ( in @ ( kpair @ X193 @ X192 ) @ X190 )
| ( in @ ( kpair @ X191 @ X192 ) @ ( breln1compset @ X188 @ X189 @ X190 ) ) )
& ( ( in @ ( esk11_5 @ X194 @ X195 @ X196 @ X197 @ X198 ) @ X194 )
| ~ ( in @ ( kpair @ X197 @ X198 ) @ ( breln1compset @ X194 @ X195 @ X196 ) )
| ~ ( in @ X198 @ X194 )
| ~ ( in @ X197 @ X194 )
| ~ ( subset @ X196 @ ( cartprod @ X194 @ X194 ) )
| ~ ( subset @ X195 @ ( cartprod @ X194 @ X194 ) ) )
& ( ( in @ ( kpair @ X197 @ ( esk11_5 @ X194 @ X195 @ X196 @ X197 @ X198 ) ) @ X195 )
| ~ ( in @ ( kpair @ X197 @ X198 ) @ ( breln1compset @ X194 @ X195 @ X196 ) )
| ~ ( in @ X198 @ X194 )
| ~ ( in @ X197 @ X194 )
| ~ ( subset @ X196 @ ( cartprod @ X194 @ X194 ) )
| ~ ( subset @ X195 @ ( cartprod @ X194 @ X194 ) ) )
& ( ( in @ ( kpair @ ( esk11_5 @ X194 @ X195 @ X196 @ X197 @ X198 ) @ X198 ) @ X196 )
| ~ ( in @ ( kpair @ X197 @ X198 ) @ ( breln1compset @ X194 @ X195 @ X196 ) )
| ~ ( in @ X198 @ X194 )
| ~ ( in @ X197 @ X194 )
| ~ ( subset @ X196 @ ( cartprod @ X194 @ X194 ) )
| ~ ( subset @ X195 @ ( cartprod @ X194 @ X194 ) ) )
& ( subset @ esk13_0 @ ( cartprod @ esk12_0 @ esk12_0 ) )
& ( subset @ esk14_0 @ ( cartprod @ esk12_0 @ esk12_0 ) )
& ( in @ esk15_0 @ esk12_0 )
& ( in @ esk16_0 @ esk12_0 )
& ( in @ ( kpair @ esk15_0 @ esk16_0 ) @ ( breln1compset @ esk12_0 @ esk13_0 @ esk14_0 ) )
& ( ~ ( in @ X206 @ esk12_0 )
| ~ ( in @ ( kpair @ esk15_0 @ X206 ) @ esk13_0 )
| ~ ( in @ ( kpair @ X206 @ esk16_0 ) @ esk14_0 )
| epred1_0 )
& ~ epred1_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_23])])])])])]) ).
thf(c_0_25,negated_conjecture,
! [X2: $i] :
( epred1_0
| ~ ( in @ X2 @ esk12_0 )
| ~ ( in @ ( kpair @ esk15_0 @ X2 ) @ esk13_0 )
| ~ ( in @ ( kpair @ X2 @ esk16_0 ) @ esk14_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_26,negated_conjecture,
~ epred1_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_27,negated_conjecture,
! [X7: $i,X5: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk11_5 @ X2 @ X3 @ X4 @ X5 @ X7 ) @ X7 ) @ X4 )
| ~ ( in @ ( kpair @ X5 @ X7 ) @ ( breln1compset @ X2 @ X3 @ X4 ) )
| ~ ( in @ X7 @ X2 )
| ~ ( in @ X5 @ X2 )
| ~ ( subset @ X4 @ ( cartprod @ X2 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X2 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_28,negated_conjecture,
in @ ( kpair @ esk15_0 @ esk16_0 ) @ ( breln1compset @ esk12_0 @ esk13_0 @ esk14_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,negated_conjecture,
subset @ esk14_0 @ ( cartprod @ esk12_0 @ esk12_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_30,negated_conjecture,
subset @ esk13_0 @ ( cartprod @ esk12_0 @ esk12_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_31,negated_conjecture,
in @ esk16_0 @ esk12_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_32,negated_conjecture,
in @ esk15_0 @ esk12_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_33,negated_conjecture,
! [X2: $i,X7: $i,X5: $i,X4: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ ( esk11_5 @ X3 @ X4 @ X5 @ X2 @ X7 ) ) @ X4 )
| ~ ( in @ ( kpair @ X2 @ X7 ) @ ( breln1compset @ X3 @ X4 @ X5 ) )
| ~ ( in @ X7 @ X3 )
| ~ ( in @ X2 @ X3 )
| ~ ( subset @ X5 @ ( cartprod @ X3 @ X3 ) )
| ~ ( subset @ X4 @ ( cartprod @ X3 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_34,negated_conjecture,
! [X7: $i,X5: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk11_5 @ X2 @ X3 @ X4 @ X5 @ X7 ) @ X2 )
| ~ ( in @ ( kpair @ X5 @ X7 ) @ ( breln1compset @ X2 @ X3 @ X4 ) )
| ~ ( in @ X7 @ X2 )
| ~ ( in @ X5 @ X2 )
| ~ ( subset @ X4 @ ( cartprod @ X2 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X2 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_35,negated_conjecture,
! [X2: $i] :
( ~ ( in @ ( kpair @ X2 @ esk16_0 ) @ esk14_0 )
| ~ ( in @ ( kpair @ esk15_0 @ X2 ) @ esk13_0 )
| ~ ( in @ X2 @ esk12_0 ) ),
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_36,negated_conjecture,
in @ ( kpair @ ( esk11_5 @ esk12_0 @ esk13_0 @ esk14_0 @ esk15_0 @ esk16_0 ) @ esk16_0 ) @ esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]) ).
thf(c_0_37,negated_conjecture,
in @ ( kpair @ esk15_0 @ ( esk11_5 @ esk12_0 @ esk13_0 @ esk14_0 @ esk15_0 @ esk16_0 ) ) @ esk13_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]) ).
thf(c_0_38,negated_conjecture,
in @ ( esk11_5 @ esk12_0 @ esk13_0 @ esk14_0 @ esk15_0 @ esk16_0 ) @ esk12_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]) ).
thf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU781^1 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 16:45:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.50 Running higher-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.21/0.58 # Version: 3.1.0-ho
% 0.21/0.58 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.58 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.58 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.58 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.58 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.58 # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.58 # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.58 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.58 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.58 # Starting new_ho_5 with 300s (1) cores
% 0.21/0.58 # new_ho_5 with pid 6030 completed with status 0
% 0.21/0.58 # Result found by new_ho_5
% 0.21/0.58 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.58 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.58 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.58 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.58 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.58 # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.58 # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.58 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.58 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.58 # Starting new_ho_5 with 300s (1) cores
% 0.21/0.58 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.21/0.58 # Search class: HGUSF-FSMM33-SHFMMFBN
% 0.21/0.58 # partial match(5): HGHSM-FSLM31-SHFMMSBN
% 0.21/0.58 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.58 # Starting ehoh_best3 with 163s (1) cores
% 0.21/0.58 # ehoh_best3 with pid 6031 completed with status 0
% 0.21/0.58 # Result found by ehoh_best3
% 0.21/0.58 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.58 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.58 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.58 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.58 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.58 # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.58 # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.58 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.58 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.58 # Starting new_ho_5 with 300s (1) cores
% 0.21/0.58 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.21/0.58 # Search class: HGUSF-FSMM33-SHFMMFBN
% 0.21/0.58 # partial match(5): HGHSM-FSLM31-SHFMMSBN
% 0.21/0.58 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.58 # Starting ehoh_best3 with 163s (1) cores
% 0.21/0.58 # Preprocessing time : 0.003 s
% 0.21/0.58 # Presaturation interreduction done
% 0.21/0.58
% 0.21/0.58 # Proof found!
% 0.21/0.58 # SZS status Theorem
% 0.21/0.58 # SZS output start CNFRefutation
% See solution above
% 0.21/0.58 # Parsed axioms : 647
% 0.21/0.58 # Removed by relevancy pruning/SinE : 636
% 0.21/0.58 # Initial clauses : 330
% 0.21/0.58 # Removed in clause preprocessing : 0
% 0.21/0.58 # Initial clauses in saturation : 330
% 0.21/0.58 # Processed clauses : 684
% 0.21/0.58 # ...of these trivial : 0
% 0.21/0.58 # ...subsumed : 0
% 0.21/0.58 # ...remaining for further processing : 684
% 0.21/0.58 # Other redundant clauses eliminated : 0
% 0.21/0.58 # Clauses deleted for lack of memory : 0
% 0.21/0.58 # Backward-subsumed : 0
% 0.21/0.58 # Backward-rewritten : 0
% 0.21/0.58 # Generated clauses : 100
% 0.21/0.58 # ...of the previous two non-redundant : 99
% 0.21/0.58 # ...aggressively subsumed : 0
% 0.21/0.58 # Contextual simplify-reflections : 0
% 0.21/0.58 # Paramodulations : 100
% 0.21/0.58 # Factorizations : 0
% 0.21/0.58 # NegExts : 0
% 0.21/0.58 # Equation resolutions : 0
% 0.21/0.58 # Disequality decompositions : 0
% 0.21/0.58 # Total rewrite steps : 14
% 0.21/0.58 # ...of those cached : 8
% 0.21/0.58 # Propositional unsat checks : 0
% 0.21/0.58 # Propositional check models : 0
% 0.21/0.58 # Propositional check unsatisfiable : 0
% 0.21/0.58 # Propositional clauses : 0
% 0.21/0.58 # Propositional clauses after purity: 0
% 0.21/0.58 # Propositional unsat core size : 0
% 0.21/0.58 # Propositional preprocessing time : 0.000
% 0.21/0.58 # Propositional encoding time : 0.000
% 0.21/0.58 # Propositional solver time : 0.000
% 0.21/0.58 # Success case prop preproc time : 0.000
% 0.21/0.58 # Success case prop encoding time : 0.000
% 0.21/0.58 # Success case prop solver time : 0.000
% 0.21/0.58 # Current number of processed clauses : 354
% 0.21/0.58 # Positive orientable unit clauses : 298
% 0.21/0.58 # Positive unorientable unit clauses: 0
% 0.21/0.58 # Negative unit clauses : 1
% 0.21/0.58 # Non-unit-clauses : 55
% 0.21/0.58 # Current number of unprocessed clauses: 71
% 0.21/0.58 # ...number of literals in the above : 302
% 0.21/0.58 # Current number of archived formulas : 0
% 0.21/0.58 # Current number of archived clauses : 330
% 0.21/0.58 # Clause-clause subsumption calls (NU) : 899
% 0.21/0.58 # Rec. Clause-clause subsumption calls : 102
% 0.21/0.58 # Non-unit clause-clause subsumptions : 0
% 0.21/0.58 # Unit Clause-clause subsumption calls : 2
% 0.21/0.58 # Rewrite failures with RHS unbound : 0
% 0.21/0.58 # BW rewrite match attempts : 0
% 0.21/0.58 # BW rewrite match successes : 0
% 0.21/0.58 # Condensation attempts : 0
% 0.21/0.58 # Condensation successes : 0
% 0.21/0.58 # Termbank termtop insertions : 25710
% 0.21/0.58 # Search garbage collected termcells : 8768
% 0.21/0.58
% 0.21/0.58 # -------------------------------------------------
% 0.21/0.58 # User time : 0.036 s
% 0.21/0.58 # System time : 0.010 s
% 0.21/0.58 # Total time : 0.046 s
% 0.21/0.58 # Maximum resident set size: 4600 pages
% 0.21/0.58
% 0.21/0.58 # -------------------------------------------------
% 0.21/0.58 # User time : 0.054 s
% 0.21/0.58 # System time : 0.015 s
% 0.21/0.58 # Total time : 0.068 s
% 0.21/0.58 # Maximum resident set size: 2504 pages
% 0.21/0.58 % E---3.1 exiting
% 0.21/0.58 % E exiting
%------------------------------------------------------------------------------