%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU662^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:35 AM UTC 2026
% Result : Theorem 0.19s 0.34s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 3341 ( 934 equ; 0 cnn)
% Maximal formula atoms : 181 ( 98 avg)
% Number of connectives : 1589 ( 27 ~; 17 |; 723 &; 98 @)
% ( 4 <=>; 720 =>; 0 <=; 0 <~>)
% Maximal formula depth : 188 ( 46 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 346 ( 343 usr; 198 con; 0-4 aty)
% Number of variables : 48 ( 0 sgn 32 !; 16 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_212,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_213,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_214,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_215,type,
vAND: $o > $o > $o ).
thf(func_def_216,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_217,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_218,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_219,type,
vIMP: $o > $o > $o ).
thf(func_def_220,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_221,type,
vNOT: $o > $o ).
thf(func_def_222,type,
sP0: $i > $i > $o ).
thf(func_def_223,type,
sP1: $i > $o ).
thf(func_def_224,type,
sP2: $o ).
thf(func_def_240,type,
sK18: $i > $i > $i ).
thf(func_def_247,type,
sK25: $i > $i > $i ).
thf(func_def_254,type,
sK32: ( $i > $o ) > $i > $i ).
thf(func_def_256,type,
sK34: $i > $o ).
thf(func_def_261,type,
sK39: $o ).
thf(func_def_287,type,
sK65: $i > $i > $i ).
thf(func_def_292,type,
sK70: $i > ( $i > $o ) > $i ).
thf(func_def_293,type,
sK71: $i > $o ).
thf(func_def_305,type,
sK83: $i > $o ).
thf(func_def_308,type,
sK86: $i > $i ).
thf(func_def_309,type,
sK87: $i > ( $i > $o ) > $i ).
thf(func_def_310,type,
sK88: $i > $o ).
thf(func_def_315,type,
sK93: $i > $i ).
thf(func_def_316,type,
sK94: $i > ( $i > $o ) > $i ).
thf(func_def_317,type,
sK95: $i > $o ).
thf(func_def_326,type,
sK104: $i > $o ).
thf(func_def_334,type,
sK112: $i > $o ).
thf(func_def_344,type,
sK122: $o ).
thf(func_def_345,type,
sK123: $i > $i > $i ).
thf(func_def_349,type,
sK127: $o ).
thf(func_def_351,type,
sK129: $i > $o ).
thf(func_def_354,type,
sK132: $i > ( $i > $o ) > $i ).
thf(func_def_355,type,
sK133: $i > ( $i > $o ) > $i ).
thf(func_def_356,type,
sK134: $i > $o ).
thf(func_def_359,type,
sK137: $i > $o ).
thf(func_def_361,type,
sK139: ( $i > $o ) > $i > $i ).
thf(func_def_362,type,
sK140: ( $i > $o ) > $i > $i ).
thf(func_def_376,type,
sK154: $i > $i > $i ).
thf(func_def_384,type,
sK162: $o ).
thf(func_def_394,type,
sK172: $i > $o ).
thf(func_def_400,type,
sK178: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_401,type,
sK179: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_402,type,
sK180: $i > $o ).
thf(func_def_403,type,
sK181: $i > $o ).
thf(func_def_408,type,
sK186: ( $i > $o ) > $i ).
thf(func_def_409,type,
sK187: $i > $o ).
thf(func_def_410,type,
sK188: $i > $i ).
thf(func_def_419,type,
sK197: $i > $i > $i ).
thf(func_def_422,type,
sK200: $i > $i ).
thf(func_def_441,type,
sK219: $o ).
thf(func_def_445,type,
sK223: $i > $o ).
thf(func_def_460,type,
sK238: $o ).
thf(func_def_468,type,
sK246: $i > $i ).
thf(func_def_470,type,
sK248: $i > $i ).
thf(func_def_473,type,
sK251: ( $i > $o ) > $i > $i ).
thf(func_def_475,type,
sK253: $i > $o ).
thf(func_def_478,type,
sK256: $i > $o ).
thf(func_def_479,type,
sK257: $i > $i ).
thf(func_def_480,type,
sK258: ( $i > $o ) > $i ).
thf(func_def_485,type,
sK263: $i > $i > $i ).
thf(func_def_491,type,
sK269: $i > $o ).
thf(func_def_494,type,
sK272: $i > $i > $o ).
thf(func_def_495,type,
sK273: $i > $i ).
thf(func_def_496,type,
sK274: $i > $i ).
thf(func_def_497,type,
sK275: ( $i > $i > $o ) > $i > $i ).
thf(func_def_498,type,
sK276: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_499,type,
sK277: ( $i > $i > $o ) > $i > $i ).
thf(func_def_513,type,
sK291: $i > $o ).
thf(func_def_521,type,
sK299: $i > ( $i > $o ) > $i ).
thf(func_def_522,type,
sK300: $i > $o ).
thf(func_def_541,type,
sK319: $i > $i > $i > $i ).
thf(func_def_542,type,
sK320: $i > $i > $i > $i ).
thf(func_def_546,type,
sK324: $i > $o ).
thf(func_def_551,type,
sK329: $i > $o ).
thf(func_def_558,type,
sK336: ( $i > $o ) > $i > $i ).
thf(func_def_560,type,
sK338: $i > $o ).
thf(func_def_565,type,
sK343: ( $i > $o ) > $i ).
thf(func_def_566,type,
sK344: ( $i > $o ) > $i ).
thf(func_def_567,type,
sK345: $i > $o ).
thf(func_def_585,type,
sK363: $i > $o ).
thf(func_def_592,type,
sK370: $i > $i ).
thf(func_def_593,type,
sK371: $i > $o ).
thf(func_def_596,type,
sK374: $i > ( $i > $o ) > $i ).
thf(func_def_597,type,
sK375: $i > ( $i > $o ) > $i ).
thf(func_def_598,type,
sK376: $o > $i > $i > $i ).
thf(func_def_601,type,
sK379: $o ).
thf(func_def_606,type,
sK384: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_607,type,
sK385: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_608,type,
sK386: $i > $o ).
thf(func_def_609,type,
sK387: $i > $o ).
thf(func_def_614,type,
sK392: $i > $i ).
thf(func_def_632,type,
sK410: $i > $i > $i ).
thf(func_def_638,type,
sK416: $i > $o ).
thf(func_def_639,type,
sK417: $o ).
thf(func_def_648,type,
sK426: $i > $i > $i ).
thf(func_def_649,type,
sK427: $i > $i > $i ).
thf(func_def_652,type,
sK430: ( $i > $o ) > $i > $i > $i ).
thf(func_def_655,type,
sK433: $i > $o ).
thf(func_def_662,type,
sK440: $i > $o ).
thf(func_def_674,type,
sK452: $i > $o ).
thf(func_def_675,type,
sK453: ( $i > $o ) > $i ).
thf(func_def_685,type,
sK463: $i > $o ).
thf(func_def_686,type,
sK464: $i > $o ).
thf(func_def_687,type,
sK465: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_688,type,
sK466: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_690,type,
sK468: $i > $i ).
thf(func_def_691,type,
sK469: $i > $i ).
thf(func_def_692,type,
sK470: $i > $i ).
thf(func_def_693,type,
sK471: $i > $i ).
thf(func_def_694,type,
sK472: $i > $i ).
thf(func_def_695,type,
sK473: $i > $i > $i > $i ).
thf(func_def_696,type,
sK474: $i > $i ).
thf(func_def_697,type,
sK475: $i > $i ).
thf(func_def_698,type,
sK476: $i > $i ).
thf(func_def_699,type,
sK477: $i > $i ).
thf(func_def_700,type,
sK478: $i > $i > $i ).
thf(func_def_701,type,
sK479: $i > $i > $i ).
thf(func_def_702,type,
sK480: $i > $i > $i > $i ).
thf(func_def_703,type,
sK481: $i > $i > $i > $i ).
thf(func_def_704,type,
sK482: $i > $i > $i > $i ).
thf(func_def_705,type,
sK483: $i > $i > $i ).
thf(func_def_706,type,
sK484: $i > $i > $i ).
thf(func_def_707,type,
sK485: $i > $i > $i ).
thf(f166,axiom,
! [X0: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 )
= kfstpairEq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(f183,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
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(f184,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
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f183]) ).
thf(f305,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( 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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( kfst @ ( kpair @ X0 @ X3 ) )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f184]) ).
thf(f306,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( kfst @ ( kpair @ X0 @ X3 ) )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f305]) ).
thf(f387,plain,
( ( kfstpairEq = $true )
<=> ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ),
inference(fool_elimination,[],[f166]) ).
thf(f730,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( kfst @ ( kpair @ X0 @ X3 ) )
!= X0 ) )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f306]) ).
thf(f731,plain,
( ( subsetTrans = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg2 = $true )
& ( setunionE = $true )
& ( setadjoinAx = $true )
& ( setminusELneg = $true )
& ( powersetAx = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIL = $true )
& ( cartprodmempair1 = $true )
& ( omegaSAx = $true )
& ( ubforcartprodlem3 = $true )
& ( binintersectI = $true )
& ( setminusI = $true )
& ( upairsubunion = $true )
& ( setadjoinSub2 = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL1 = $true )
& ( quantDeMorgan4 = $true )
& ( exuE3u = $true )
& ( inPowerset = $true )
& ( ex1E1 = $true )
& ( notdallE = $true )
& ( exuEu = $true )
& ( eqimpsubset2 = $true )
& ( subsetE = $true )
& ( emptysetimpfalse = $true )
& ( inCongP = $true )
& ( powersetE = $true )
& ( setunionAx = $true )
& ( kfstsingleton = $true )
& ( setextsub = $true )
& ( powersetI1 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyI1 = $true )
& ( binunionRsub = $true )
& ( emptysetsubset = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( prop2setI = $true )
& ( symdiffI2 = $true )
& ( emptysetAx = $true )
& ( setukpairinjR11 = $true )
& ( cartprodfstin = $true )
& ( omegaIndAx = $true )
& ( setadjoinOr = $true )
& ( cartprodpairin = $true )
& ( setadjoin__Cong = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( symdiffE = $true )
& ( setbeta = $true )
& ( sepInPowerset = $true )
& ( emptyI = $true )
& ( cartprodpairmemER = $true )
& ( eqinunit = $true )
& ( setadjoinSub = $true )
& ( subsetE2 = $true )
& ( symdiffI1 = $true )
& ( cartprodpairmemEL = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR12 = $true )
& ( powersetE1 = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan1 = $true )
& ( notinsingleton = $true )
& ( symdiffIneg1 = $true )
& ( emptyinPowerset = $true )
& ( setukpairinjL = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( kfst @ ( kpair @ X0 @ X3 ) )
!= X0 ) )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( powersetsubset = $true )
& ( emptyset__Cong = $true )
& ( notdexE = $true )
& ( ex1I2 = $true )
& ( subset2powerset = $true )
& ( setukpairIR = $true )
& ( setminusERneg = $true )
& ( descrp = $true )
& ( upairset2E = $true )
& ( subsetRefl = $true )
& ( singletoninpowunion = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodmempaircEq = $true )
& ( emptyInPowerset = $true )
& ( binintersectRsub = $true )
& ( ex1I = $true )
& ( setadjoinIR = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( upairsetIR = $true )
& ( prop2setE = $true )
& ( sepSubset = $true )
& ( setminusEL = $true )
& ( binintersectEL = $true )
& ( emptysetE = $true )
& ( emptyE1 = $true )
& ( subsetI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset1 = $true )
& ( binunionE = $true )
& ( setminusSubset2 = $true )
& ( powerset__Cong = $true )
& ( upairinpowunion = $true )
& ( notinemptyset = $true )
& ( upairsetIL = $true )
& ( nonemptyI = $true )
& ( setextAx = $true )
& ( setminusLsub = $true )
& ( singletonprop = $true )
& ( setunionI = $true )
& ( singletonsuniq = $true )
& ( exu__Cong = $true )
& ( setunionE2 = $true )
& ( powersetI = $true )
& ( notsubsetI = $true )
& ( eqimpsubset1 = $true )
& ( kpairsurjEq = $true )
& ( exuE2 = $true )
& ( setunionsingleton2 = $true )
& ( binintersectSubset3 = $true )
& ( exuE3e = $true )
& ( wellorderingAx = $true )
& ( kpairiskpair = $true )
& ( ksndsingleton = $true )
& ( bs114d = $true )
& ( kfstpairEq = $true )
& ( setunionsingleton = $true )
& ( setukpairinjR = $true )
& ( notequalI1 = $true )
& ( upairset2IR = $true )
& ( uniqinunit = $true )
& ( setunionsingleton1 = $true )
& ( in__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( setukpairinjR2 = $true )
& ( binintersectSubset1 = $true )
& ( upairsetE = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( emptyinunitempty = $true )
& ( binunionLsub = $true )
& ( cartprodsndin = $true )
& ( exuE1 = $true )
& ( disjointsetsI1 = $true )
& ( setminusER = $true )
& ( binunionIR = $true )
& ( setukpairIL = $true )
& ( kpairp = $true )
& ( dsetconstr__Cong = $true )
& ( binunionEcases = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstrER = $true )
& ( subsetI2 = $true )
& ( subPowSU = $true )
& ( replAx = $true )
& ( notequalI2 = $true )
& ( exuI1 = $true )
& ( setukpairinjL2 = $true )
& ( ksndpairEq = $true )
& ( theprop = $true )
& ( binintersectLsub = $true )
& ( subsetemptysetimpeq = $true )
& ( setoftrueEq = $true )
& ( singletonsubset = $true )
& ( secondinupair = $true )
& ( binintersectSubset2 = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ( setminusIRneg = $true )
& ( binunionIL = $true )
& ( setext = $true )
& ( setadjoinE = $true )
& ( cartprodmempair = $true ) ),
inference(flattening,[],[f730]) ).
thf(f915,plain,
( ( ( kfstpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
!= X0 ) )
& ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 )
| ( kfstpairEq != $true ) ) ),
inference(nnf_transformation,[],[f387]) ).
thf(f916,plain,
( ( ( kfstpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
!= X0 ) )
& ( ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ( kfstpairEq != $true ) ) ),
inference(rectify,[],[f915]) ).
thf(f917,plain,
( ( ( kfstpairEq = $true )
| ( ( kfst @ ( kpair @ sK145 @ sK146 ) )
!= sK145 ) )
& ( ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ( kfstpairEq != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145,sK146]),skolemize(X0,sK145),skolemize(X1,sK146)],[f916]) ).
thf(f942,plain,
( ( subsetTrans = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg2 = $true )
& ( setunionE = $true )
& ( setadjoinAx = $true )
& ( setminusELneg = $true )
& ( powersetAx = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIL = $true )
& ( cartprodmempair1 = $true )
& ( omegaSAx = $true )
& ( ubforcartprodlem3 = $true )
& ( binintersectI = $true )
& ( setminusI = $true )
& ( upairsubunion = $true )
& ( setadjoinSub2 = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL1 = $true )
& ( quantDeMorgan4 = $true )
& ( exuE3u = $true )
& ( inPowerset = $true )
& ( ex1E1 = $true )
& ( notdallE = $true )
& ( exuEu = $true )
& ( eqimpsubset2 = $true )
& ( subsetE = $true )
& ( emptysetimpfalse = $true )
& ( inCongP = $true )
& ( powersetE = $true )
& ( setunionAx = $true )
& ( kfstsingleton = $true )
& ( setextsub = $true )
& ( powersetI1 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyI1 = $true )
& ( binunionRsub = $true )
& ( emptysetsubset = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( prop2setI = $true )
& ( symdiffI2 = $true )
& ( emptysetAx = $true )
& ( setukpairinjR11 = $true )
& ( cartprodfstin = $true )
& ( omegaIndAx = $true )
& ( setadjoinOr = $true )
& ( cartprodpairin = $true )
& ( setadjoin__Cong = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( symdiffE = $true )
& ( setbeta = $true )
& ( sepInPowerset = $true )
& ( emptyI = $true )
& ( cartprodpairmemER = $true )
& ( eqinunit = $true )
& ( setadjoinSub = $true )
& ( subsetE2 = $true )
& ( symdiffI1 = $true )
& ( cartprodpairmemEL = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR12 = $true )
& ( powersetE1 = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan1 = $true )
& ( notinsingleton = $true )
& ( symdiffIneg1 = $true )
& ( emptyinPowerset = $true )
& ( setukpairinjL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( kfst @ ( kpair @ X2 @ X3 ) )
!= X2 ) )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( powersetsubset = $true )
& ( emptyset__Cong = $true )
& ( notdexE = $true )
& ( ex1I2 = $true )
& ( subset2powerset = $true )
& ( setukpairIR = $true )
& ( setminusERneg = $true )
& ( descrp = $true )
& ( upairset2E = $true )
& ( subsetRefl = $true )
& ( singletoninpowunion = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodmempaircEq = $true )
& ( emptyInPowerset = $true )
& ( binintersectRsub = $true )
& ( ex1I = $true )
& ( setadjoinIR = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( upairsetIR = $true )
& ( prop2setE = $true )
& ( sepSubset = $true )
& ( setminusEL = $true )
& ( binintersectEL = $true )
& ( emptysetE = $true )
& ( emptyE1 = $true )
& ( subsetI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset1 = $true )
& ( binunionE = $true )
& ( setminusSubset2 = $true )
& ( powerset__Cong = $true )
& ( upairinpowunion = $true )
& ( notinemptyset = $true )
& ( upairsetIL = $true )
& ( nonemptyI = $true )
& ( setextAx = $true )
& ( setminusLsub = $true )
& ( singletonprop = $true )
& ( setunionI = $true )
& ( singletonsuniq = $true )
& ( exu__Cong = $true )
& ( setunionE2 = $true )
& ( powersetI = $true )
& ( notsubsetI = $true )
& ( eqimpsubset1 = $true )
& ( kpairsurjEq = $true )
& ( exuE2 = $true )
& ( setunionsingleton2 = $true )
& ( binintersectSubset3 = $true )
& ( exuE3e = $true )
& ( wellorderingAx = $true )
& ( kpairiskpair = $true )
& ( ksndsingleton = $true )
& ( bs114d = $true )
& ( kfstpairEq = $true )
& ( setunionsingleton = $true )
& ( setukpairinjR = $true )
& ( notequalI1 = $true )
& ( upairset2IR = $true )
& ( uniqinunit = $true )
& ( setunionsingleton1 = $true )
& ( in__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( setukpairinjR2 = $true )
& ( binintersectSubset1 = $true )
& ( upairsetE = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( emptyinunitempty = $true )
& ( binunionLsub = $true )
& ( cartprodsndin = $true )
& ( exuE1 = $true )
& ( disjointsetsI1 = $true )
& ( setminusER = $true )
& ( binunionIR = $true )
& ( setukpairIL = $true )
& ( kpairp = $true )
& ( dsetconstr__Cong = $true )
& ( binunionEcases = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstrER = $true )
& ( subsetI2 = $true )
& ( subPowSU = $true )
& ( replAx = $true )
& ( notequalI2 = $true )
& ( exuI1 = $true )
& ( setukpairinjL2 = $true )
& ( ksndpairEq = $true )
& ( theprop = $true )
& ( binintersectLsub = $true )
& ( subsetemptysetimpeq = $true )
& ( setoftrueEq = $true )
& ( singletonsubset = $true )
& ( secondinupair = $true )
& ( binintersectSubset2 = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ( setminusIRneg = $true )
& ( binunionIL = $true )
& ( setext = $true )
& ( setadjoinE = $true )
& ( cartprodmempair = $true ) ),
inference(rectify,[],[f731]) ).
thf(f943,plain,
( ( subsetTrans = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg2 = $true )
& ( setunionE = $true )
& ( setadjoinAx = $true )
& ( setminusELneg = $true )
& ( powersetAx = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIL = $true )
& ( cartprodmempair1 = $true )
& ( omegaSAx = $true )
& ( ubforcartprodlem3 = $true )
& ( binintersectI = $true )
& ( setminusI = $true )
& ( upairsubunion = $true )
& ( setadjoinSub2 = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL1 = $true )
& ( quantDeMorgan4 = $true )
& ( exuE3u = $true )
& ( inPowerset = $true )
& ( ex1E1 = $true )
& ( notdallE = $true )
& ( exuEu = $true )
& ( eqimpsubset2 = $true )
& ( subsetE = $true )
& ( emptysetimpfalse = $true )
& ( inCongP = $true )
& ( powersetE = $true )
& ( setunionAx = $true )
& ( kfstsingleton = $true )
& ( setextsub = $true )
& ( powersetI1 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyI1 = $true )
& ( binunionRsub = $true )
& ( emptysetsubset = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( prop2setI = $true )
& ( symdiffI2 = $true )
& ( emptysetAx = $true )
& ( setukpairinjR11 = $true )
& ( cartprodfstin = $true )
& ( omegaIndAx = $true )
& ( setadjoinOr = $true )
& ( cartprodpairin = $true )
& ( setadjoin__Cong = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( symdiffE = $true )
& ( setbeta = $true )
& ( sepInPowerset = $true )
& ( emptyI = $true )
& ( cartprodpairmemER = $true )
& ( eqinunit = $true )
& ( setadjoinSub = $true )
& ( subsetE2 = $true )
& ( symdiffI1 = $true )
& ( cartprodpairmemEL = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR12 = $true )
& ( powersetE1 = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan1 = $true )
& ( notinsingleton = $true )
& ( symdiffIneg1 = $true )
& ( emptyinPowerset = $true )
& ( setukpairinjL = $true )
& ( $true
= ( in @ sK171 @ sK168 ) )
& ( sK170
!= ( kfst @ ( kpair @ sK170 @ sK171 ) ) )
& ( $true
= ( in @ sK170 @ sK169 ) )
& ( powersetsubset = $true )
& ( emptyset__Cong = $true )
& ( notdexE = $true )
& ( ex1I2 = $true )
& ( subset2powerset = $true )
& ( setukpairIR = $true )
& ( setminusERneg = $true )
& ( descrp = $true )
& ( upairset2E = $true )
& ( subsetRefl = $true )
& ( singletoninpowunion = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodmempaircEq = $true )
& ( emptyInPowerset = $true )
& ( binintersectRsub = $true )
& ( ex1I = $true )
& ( setadjoinIR = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( upairsetIR = $true )
& ( prop2setE = $true )
& ( sepSubset = $true )
& ( setminusEL = $true )
& ( binintersectEL = $true )
& ( emptysetE = $true )
& ( emptyE1 = $true )
& ( subsetI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset1 = $true )
& ( binunionE = $true )
& ( setminusSubset2 = $true )
& ( powerset__Cong = $true )
& ( upairinpowunion = $true )
& ( notinemptyset = $true )
& ( upairsetIL = $true )
& ( nonemptyI = $true )
& ( setextAx = $true )
& ( setminusLsub = $true )
& ( singletonprop = $true )
& ( setunionI = $true )
& ( singletonsuniq = $true )
& ( exu__Cong = $true )
& ( setunionE2 = $true )
& ( powersetI = $true )
& ( notsubsetI = $true )
& ( eqimpsubset1 = $true )
& ( kpairsurjEq = $true )
& ( exuE2 = $true )
& ( setunionsingleton2 = $true )
& ( binintersectSubset3 = $true )
& ( exuE3e = $true )
& ( wellorderingAx = $true )
& ( kpairiskpair = $true )
& ( ksndsingleton = $true )
& ( bs114d = $true )
& ( kfstpairEq = $true )
& ( setunionsingleton = $true )
& ( setukpairinjR = $true )
& ( notequalI1 = $true )
& ( upairset2IR = $true )
& ( uniqinunit = $true )
& ( setunionsingleton1 = $true )
& ( in__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( setukpairinjR2 = $true )
& ( binintersectSubset1 = $true )
& ( upairsetE = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( emptyinunitempty = $true )
& ( binunionLsub = $true )
& ( cartprodsndin = $true )
& ( exuE1 = $true )
& ( disjointsetsI1 = $true )
& ( setminusER = $true )
& ( binunionIR = $true )
& ( setukpairIL = $true )
& ( kpairp = $true )
& ( dsetconstr__Cong = $true )
& ( binunionEcases = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstrER = $true )
& ( subsetI2 = $true )
& ( subPowSU = $true )
& ( replAx = $true )
& ( notequalI2 = $true )
& ( exuI1 = $true )
& ( setukpairinjL2 = $true )
& ( ksndpairEq = $true )
& ( theprop = $true )
& ( binintersectLsub = $true )
& ( subsetemptysetimpeq = $true )
& ( setoftrueEq = $true )
& ( singletonsubset = $true )
& ( secondinupair = $true )
& ( binintersectSubset2 = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ( setminusIRneg = $true )
& ( binunionIL = $true )
& ( setext = $true )
& ( setadjoinE = $true )
& ( cartprodmempair = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168,sK169,sK170,sK171]),skolemize(X0,sK168),skolemize(X1,sK169),skolemize(X2,sK170),skolemize(X3,sK171)],[f942]) ).
thf(f1495,plain,
! [X2: $i,X3: $i] :
( ( kfstpairEq != $true )
| ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
inference(cnf_transformation,[],[f917]) ).
thf(f1577,plain,
kfstpairEq = $true,
inference(cnf_transformation,[],[f943]) ).
thf(f1634,plain,
( sK170
!= ( kfst @ ( kpair @ sK170 @ sK171 ) ) ),
inference(cnf_transformation,[],[f943]) ).
thf(f3197,definition,
( spl497_196
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[spl497_196])],[avatar_definition]) ).
thf(f3198,plain,
( ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ~ spl497_196 ),
inference(avatar_component_clause,[],[f3197]) ).
thf(f3200,definition,
( spl497_197
<=> ( kfstpairEq = $true ) ),
introduced(definition,[new_symbols(definition,[spl497_197])],[avatar_definition]) ).
thf(f3203,plain,
( spl497_196
| ~ spl497_197 ),
inference(avatar_split_clause,[],[f1495,f3200,f3197]) ).
thf(f3724,plain,
spl497_197,
inference(avatar_split_clause,[],[f1577,f3200]) ).
thf(f5539,definition,
( spl497_691
<=> ( sK170
= ( kfst @ ( kpair @ sK170 @ sK171 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl497_691])],[avatar_definition]) ).
thf(f5541,plain,
( ( sK170
!= ( kfst @ ( kpair @ sK170 @ sK171 ) ) )
| spl497_691 ),
inference(avatar_component_clause,[],[f5539]) ).
thf(f5542,plain,
~ spl497_691,
inference(avatar_split_clause,[],[f1634,f5539]) ).
thf(f6355,plain,
( ( sK170 != sK170 )
| ~ spl497_196
| spl497_691 ),
inference(superposition,[],[f5541,f3198]) ).
thf(f6356,plain,
( $false
| ~ spl497_196
| spl497_691 ),
inference(trivial_inequality_removal,[],[f6355]) ).
thf(f6357,plain,
( ~ spl497_196
| spl497_691 ),
inference(avatar_contradiction_clause,[],[f6356]) ).
cnf(s132,plain,
( spl497_196
| ~ spl497_197 ),
inference(sat_conversion,[],[f3203]) ).
cnf(s220,plain,
spl497_197,
inference(sat_conversion,[],[f3724]) ).
cnf(s658,plain,
~ spl497_691,
inference(sat_conversion,[],[f5542]) ).
cnf(s840,plain,
( ~ spl497_196
| spl497_691 ),
inference(sat_conversion,[],[f6357]) ).
cnf(s853,plain,
~ spl497_196,
inference(rat,[],[s840,s658]) ).
cnf(s991,plain,
$false,
inference(rat,[],[s132,s220,s853]) ).
thf(f6358,plain,
$false,
inference(avatar_sat_refutation,[],[s991]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU662^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:06:59 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.34 % (3209247)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.34 % (3209255)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4055554358:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.34 % (3209258)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.34 % (3209258)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.19/0.34 % (3209254)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2404918894:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.34 % (3209253)lrs+10_16_si=on:nwc=1.5:random_seed=656009884:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.34 % (3209252)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1347335627:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.34 % (3209256)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1986799567:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.34 % (3209257)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1579301621:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.34 % (3209258)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2751206301:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.34 % (3209254)Instruction limit reached!
% 0.19/0.34 % (3209254)------------------------------
% 0.19/0.34 % (3209254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (3209254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (3209254)CaDiCaL version: 2.1.3
% 0.19/0.34 % (3209254)Termination reason: Instruction limit
% 0.19/0.34 % (3209254)Termination phase: shuffling
% 0.19/0.34 % (3209254)Time elapsed: 0.002 s
% 0.19/0.34 % (3209254)Peak memory usage: 10 MB
% 0.19/0.34 % (3209254)Instructions burned: 3 (million)
% 0.19/0.34 % (3209253)Instruction limit reached!
% 0.19/0.34 % (3209253)------------------------------
% 0.19/0.34 % (3209253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (3209253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (3209253)CaDiCaL version: 2.1.3
% 0.19/0.34 % (3209253)Termination reason: Instruction limit
% 0.19/0.34 % (3209253)Termination phase: shuffling
% 0.19/0.34 % (3209253)Time elapsed: 0.009 s
% 0.19/0.34 % (3209253)Peak memory usage: 10 MB
% 0.19/0.34 % (3209253)Instructions burned: 20 (million)
% 0.19/0.34 % (3209256)Instruction limit reached!
% 0.19/0.34 % (3209256)------------------------------
% 0.19/0.34 % (3209256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (3209256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (3209256)CaDiCaL version: 2.1.3
% 0.19/0.34 % (3209256)Termination reason: Instruction limit
% 0.19/0.34 % (3209256)Termination phase: Naming
% 0.19/0.34 % (3209256)Time elapsed: 0.011 s
% 0.19/0.34 % (3209256)Peak memory usage: 11 MB
% 0.19/0.34 % (3209256)Instructions burned: 25 (million)
% 0.19/0.34 % (3209266)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3101429983:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.34 % (3209266)Instruction limit reached!
% 0.19/0.34 % (3209266)------------------------------
% 0.19/0.34 % (3209266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (3209266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (3209266)CaDiCaL version: 2.1.3
% 0.19/0.34 % (3209266)Termination reason: Instruction limit
% 0.19/0.34 % (3209266)Termination phase: shuffling
% 0.19/0.34 % (3209266)Time elapsed: 0.003 s
% 0.19/0.34 % (3209266)Peak memory usage: 10 MB
% 0.19/0.34 % (3209266)Instructions burned: 5 (million)
% 0.19/0.34 % (3209268)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.34 % (3209267)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=399005693:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.19/0.34 % (3209268)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=294625646:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/0.34 % (3209267)Instruction limit reached!
% 0.19/0.34 % (3209267)------------------------------
% 0.19/0.34 % (3209267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (3209267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (3209267)CaDiCaL version: 2.1.3
% 0.19/0.34 % (3209267)Termination reason: Instruction limit
% 0.19/0.34 % (3209267)Termination phase: shuffling
% 0.19/0.34 % (3209267)Time elapsed: 0.003 s
% 0.19/0.34 % (3209267)Peak memory usage: 10 MB
% 0.19/0.34 % (3209267)Instructions burned: 7 (million)
% 0.19/0.34 % (3209257)Instruction limit reached!
% 0.19/0.34 % (3209257)------------------------------
% 0.19/0.34 % (3209257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (3209257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (3209257)CaDiCaL version: 2.1.3
% 0.19/0.34 % (3209257)Termination reason: Instruction limit
% 0.19/0.34 % (3209257)Termination phase: Property scanning
% 0.19/0.34 % (3209257)Time elapsed: 0.035 s
% 0.19/0.34 % (3209257)Peak memory usage: 12 MB
% 0.19/0.34 % (3209257)Instructions burned: 77 (million)
% 0.19/0.34 % (3209268)Instruction limit reached!
% 0.19/0.34 % (3209268)------------------------------
% 0.19/0.34 % (3209268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (3209268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (3209268)CaDiCaL version: 2.1.3
% 0.19/0.34 % (3209268)Termination reason: Instruction limit
% 0.19/0.34 % (3209268)Termination phase: shuffling
% 0.19/0.34 % (3209268)Time elapsed: 0.008 s
% 0.19/0.34 % (3209268)Peak memory usage: 10 MB
% 0.19/0.34 % (3209268)Instructions burned: 8 (million)
% 0.19/0.34 % (3209252)Instruction limit reached!
% 0.19/0.34 % (3209252)------------------------------
% 0.19/0.34 % (3209252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (3209252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (3209252)CaDiCaL version: 2.1.3
% 0.19/0.34 % (3209252)Termination reason: Instruction limit
% 0.19/0.34 % (3209252)Termination phase: Property scanning
% 0.19/0.34 % (3209252)Time elapsed: 0.040 s
% 0.19/0.34 % (3209252)Peak memory usage: 13 MB
% 0.19/0.34 % (3209252)Instructions burned: 89 (million)
% 0.19/0.34 % (3209255) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3209247-3209255"...
% 0.19/0.34 % (3209255)...printing done.
% 0.19/0.34 % (3209255)Refutation found. Thanks to Tanya!
% 0.19/0.34 % SZS status Theorem for theBenchmark
% 0.19/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.35 % (3209255)------------------------------
% 0.19/0.35 % (3209255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (3209255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (3209255)CaDiCaL version: 2.1.3
% 0.19/0.35 % (3209255)Termination reason: Refutation
% 0.19/0.35 % (3209255)Time elapsed: 0.050 s
% 0.19/0.35 % (3209255)Peak memory usage: 17 MB
% 0.19/0.35 % (3209255)Instructions burned: 193 (million)
% 0.19/0.35 % (3209247)Success in time 0.099 s
% 0.19/0.35 % Vampire exiting
%------------------------------------------------------------------------------