%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU664^1 : 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 : n017.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 0.53s 0.44s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 22 unt; 0 typ; 7 def)
% Number of atoms : 3590 ( 999 equ; 0 cnn)
% Maximal formula atoms : 182 ( 53 avg)
% Number of connectives : 1826 ( 67 ~; 58 |; 736 &; 224 @)
% ( 11 <=>; 730 =>; 0 <=; 0 <~>)
% Maximal formula depth : 189 ( 25 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 : 353 ( 350 usr; 205 con; 0-4 aty)
% Number of variables : 69 ( 0 sgn 52 !; 17 ?; 69 :)
% 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_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_214,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_215,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_216,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_217,type,
vAND: $o > $o > $o ).
thf(func_def_218,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_219,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_220,type,
vIMP: $o > $o > $o ).
thf(func_def_221,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_222,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_223,type,
vNOT: $o > $o ).
thf(func_def_224,type,
sP0: $i > $i > $o ).
thf(func_def_225,type,
sP1: $i > $o ).
thf(func_def_226,type,
sP2: $o ).
thf(func_def_227,type,
sK3: $i > $o ).
thf(func_def_239,type,
sK15: $i > ( $i > $o ) > $i ).
thf(func_def_240,type,
sK16: $i > $o ).
thf(func_def_246,type,
sK22: $o ).
thf(func_def_270,type,
sK46: $i > $o ).
thf(func_def_273,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_274,type,
sK50: $i > ( $i > $o ) > $i ).
thf(func_def_275,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_276,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_277,type,
sK53: $i > $o ).
thf(func_def_290,type,
sK66: $i > $o ).
thf(func_def_294,type,
sK70: $i > $o ).
thf(func_def_312,type,
sK88: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_313,type,
sK89: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_314,type,
sK90: $i > $o ).
thf(func_def_315,type,
sK91: $i > $o ).
thf(func_def_321,type,
sK97: $i > $o ).
thf(func_def_323,type,
sK99: $i > $i > $i ).
thf(func_def_328,type,
sK104: $i > $o ).
thf(func_def_334,type,
sK110: $i > $i > $i ).
thf(func_def_345,type,
sK121: $i > $i ).
thf(func_def_349,type,
sK125: $i > $i > $i > $i ).
thf(func_def_350,type,
sK126: $i > $i > $i > $i ).
thf(func_def_356,type,
sK132: $i > $i > $i ).
thf(func_def_358,type,
sK134: $i > $o ).
thf(func_def_363,type,
sK139: $i > $o ).
thf(func_def_368,type,
sK144: $i > $i ).
thf(func_def_369,type,
sK145: $i > $i ).
thf(func_def_370,type,
sK146: $i > $i > $i ).
thf(func_def_371,type,
sK147: $i > $i > $i ).
thf(func_def_374,type,
sK150: $i > $i > $i ).
thf(func_def_396,type,
sK172: $o ).
thf(func_def_402,type,
sK178: $i > $o ).
thf(func_def_405,type,
sK181: $i > ( $i > $o ) > $i ).
thf(func_def_412,type,
sK188: $o ).
thf(func_def_417,type,
sK193: $i > $o ).
thf(func_def_420,type,
sK196: $i > ( $i > $o ) > $i ).
thf(func_def_440,type,
sK216: $o ).
thf(func_def_441,type,
sK217: $i > ( $i > $o ) > $i ).
thf(func_def_442,type,
sK218: $i > $o ).
thf(func_def_447,type,
sK223: ( $i > $o ) > $i > $i > $i ).
thf(func_def_450,type,
sK226: $i > $o ).
thf(func_def_457,type,
sK233: $i > $o ).
thf(func_def_458,type,
sK234: $i > $i ).
thf(func_def_459,type,
sK235: ( $i > $o ) > $i ).
thf(func_def_461,type,
sK237: $i > $i ).
thf(func_def_462,type,
sK238: $i > $i ).
thf(func_def_463,type,
sK239: $i > $i ).
thf(func_def_464,type,
sK240: $i > $i ).
thf(func_def_465,type,
sK241: $i > $i ).
thf(func_def_466,type,
sK242: $i > $i > $i > $i ).
thf(func_def_467,type,
sK243: $i > $i ).
thf(func_def_468,type,
sK244: $i > $i ).
thf(func_def_469,type,
sK245: $i > $i ).
thf(func_def_470,type,
sK246: $i > $i ).
thf(func_def_471,type,
sK247: $i > $i > $i ).
thf(func_def_472,type,
sK248: $i > $i > $i ).
thf(func_def_473,type,
sK249: $i > $i > $i > $i ).
thf(func_def_474,type,
sK250: $i > $i > $i > $i ).
thf(func_def_475,type,
sK251: $i > $i > $i > $i ).
thf(func_def_476,type,
sK252: $i > $i > $i ).
thf(func_def_477,type,
sK253: $i > $i > $i ).
thf(func_def_478,type,
sK254: $i > $i > $i ).
thf(func_def_479,type,
sK255: ( $i > $i > $o ) > $i > $i ).
thf(func_def_480,type,
sK256: ( $i > $i > $o ) > $i > $i ).
thf(func_def_481,type,
sK257: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_483,type,
sK259: $i > $i > $o ).
thf(func_def_484,type,
sK260: $i > $i ).
thf(func_def_485,type,
sK261: $i > $i ).
thf(func_def_486,type,
sK262: $i > $o ).
thf(func_def_487,type,
sK263: $i > $o ).
thf(func_def_488,type,
sK264: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_489,type,
sK265: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_490,type,
sK266: $i > $o ).
thf(func_def_494,type,
sK270: $i > $o ).
thf(func_def_495,type,
sK271: $i > $o ).
thf(func_def_496,type,
sK272: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_497,type,
sK273: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_502,type,
sK278: $o ).
thf(func_def_508,type,
sK284: $i > $o ).
thf(func_def_510,type,
sK286: ( $i > $o ) > $i > $i ).
thf(func_def_512,type,
sK288: $i > $o ).
thf(func_def_514,type,
sK290: ( $i > $o ) > $i > $i ).
thf(func_def_520,type,
sK296: $i > $i ).
thf(func_def_529,type,
sK305: $i > $o ).
thf(func_def_530,type,
sK306: ( $i > $o ) > $i ).
thf(func_def_542,type,
sK318: $i > ( $i > $o ) > $i ).
thf(func_def_543,type,
sK319: $i > $o ).
thf(func_def_546,type,
sK322: $i > $i > $i ).
thf(func_def_557,type,
sK333: $i > $i > $i ).
thf(func_def_565,type,
sK341: $i > $i ).
thf(func_def_569,type,
sK345: $i > ( $i > $o ) > $i ).
thf(func_def_570,type,
sK346: $i > $o ).
thf(func_def_594,type,
sK370: $o ).
thf(func_def_602,type,
sK378: $i > $i ).
thf(func_def_606,type,
sK382: $o ).
thf(func_def_607,type,
sK383: $o > $i > $i > $i ).
thf(func_def_619,type,
sK395: $i > $i ).
thf(func_def_624,type,
sK400: $i > $i > $i ).
thf(func_def_649,type,
sK425: $o ).
thf(func_def_650,type,
sK426: $i > $o ).
thf(func_def_658,type,
sK434: $i > $o ).
thf(func_def_664,type,
sK440: $i > $o ).
thf(func_def_677,type,
sK453: $i > $o ).
thf(func_def_684,type,
sK460: ( $i > $o ) > $i > $i ).
thf(func_def_685,type,
sK461: ( $i > $o ) > $i > $i ).
thf(func_def_687,type,
sK463: $i > $o ).
thf(func_def_693,type,
sK469: ( $i > $o ) > $i > $i ).
thf(func_def_695,type,
sK471: $i > $o ).
thf(func_def_696,type,
sK472: $i > $o ).
thf(func_def_697,type,
sK473: $i > $i ).
thf(func_def_698,type,
sK474: ( $i > $o ) > $i ).
thf(func_def_722,type,
sK498: $i > $i > $i ).
thf(f151,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( iskpair @ X2 ) )
= cartprodmempair ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(f178,axiom,
! [X0: $i] :
( ( ( iskpair @ X0 )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) )
= kpairsurjEq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(f185,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
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(f186,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
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f185]) ).
thf(f326,plain,
! [X0: $i] :
( ( ( iskpair @ X0 )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) )
= kpairsurjEq ),
inference(rectify,[],[f178]) ).
thf(f327,plain,
( ( kpairsurjEq = $true )
<=> ! [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ) ),
inference(fool_elimination,[],[f326]) ).
thf(f412,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
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( cartprod @ X0 @ X2 ) )
=> ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f186]) ).
thf(f413,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 )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( cartprod @ X0 @ X2 ) )
= $true )
=> ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f412]) ).
thf(f414,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
=> ( iskpair @ X1 ) )
= cartprodmempair ),
inference(rectify,[],[f151]) ).
thf(f415,plain,
( ( cartprodmempair = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true )
=> ( $true
= ( iskpair @ X1 ) ) ) ),
inference(fool_elimination,[],[f414]) ).
thf(f639,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X0 @ X2 ) )
= $true )
& ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
!= X1 ) )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( 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,[],[f413]) ).
thf(f640,plain,
( ( binintersectSubset3 = $true )
& ( emptyI = $true )
& ( setunionI = $true )
& ( kfstsingleton = $true )
& ( setukpairIL = $true )
& ( singletonsubset = $true )
& ( inPowerset = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( setminusSubset2 = $true )
& ( binunionIR = $true )
& ( setukpairinjL2 = $true )
& ( setunionE = $true )
& ( emptysetsubset = $true )
& ( exuE1 = $true )
& ( subsetI2 = $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset1 = $true )
& ( theprop = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X0 @ X2 ) )
= $true )
& ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
!= X1 ) )
& ( setadjoin__Cong = $true )
& ( upairsetE = $true )
& ( subsetTrans = $true )
& ( setbeta = $true )
& ( prop2setI = $true )
& ( notsubsetI = $true )
& ( binintersectI = $true )
& ( setextsub = $true )
& ( vacuousDall = $true )
& ( replAx = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem3 = $true )
& ( ex1I = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjR11 = $true )
& ( upairsubunion = $true )
& ( setminusERneg = $true )
& ( exuE3u = $true )
& ( setminusI = $true )
& ( notinsingleton = $true )
& ( binintersectEL = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( binunionLsub = $true )
& ( symdiffIneg1 = $true )
& ( emptyinunitempty = $true )
& ( inCongP = $true )
& ( singletonsuniq = $true )
& ( singletoninpowerset = $true )
& ( exuI3 = $true )
& ( ex1E1 = $true )
& ( subsetE2 = $true )
& ( disjointsetsI1 = $true )
& ( subset2powerset = $true )
& ( ex1I2 = $true )
& ( kfstpairEq = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodfstpairEq = $true )
& ( setadjoinIL = $true )
& ( symdiffE = $true )
& ( emptyE1 = $true )
& ( cartprodsndin = $true )
& ( setunionsingleton1 = $true )
& ( eqimpsubset1 = $true )
& ( uniqinunit = $true )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( sepSubset = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( notequalI2 = $true )
& ( binunionE = $true )
& ( quantDeMorgan1 = $true )
& ( singletonprop = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrEL = $true )
& ( binunionRsub = $true )
& ( setadjoinIR = $true )
& ( kpairiskpair = $true )
& ( upairset2E = $true )
& ( binintersectSubset4 = $true )
& ( singletonsswitch = $true )
& ( upairinpowunion = $true )
& ( secondinupair = $true )
& ( setminusER = $true )
& ( symdiffIneg2 = $true )
& ( subsetE = $true )
& ( binintersectSubset2 = $true )
& ( dsetconstrER = $true )
& ( setminusIRneg = $true )
& ( symdiffI2 = $true )
& ( notdexE = $true )
& ( exuE2 = $true )
& ( binintersectER = $true )
& ( bs114d = $true )
& ( upairequniteq = $true )
& ( binintersectSubset5 = $true )
& ( kpairp = $true )
& ( powersetsubset = $true )
& ( binintersectRsub = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( cartprodfstin = $true )
& ( exuI2 = $true )
& ( in__Cong = $true )
& ( omega__Cong = $true )
& ( setukpairIR = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairinjL1 = $true )
& ( noeltsimpempty = $true )
& ( setunion__Cong = $true )
& ( binunionEcases = $true )
& ( subsetI1 = $true )
& ( descr__Cong = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstr__Cong = $true )
& ( powersetI1 = $true )
& ( notequalI1 = $true )
& ( setunionE2 = $true )
& ( setminusELneg = $true )
& ( setadjoinSub = $true )
& ( setextAx = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetE = $true )
& ( ksndpairEq = $true )
& ( kpairsurjEq = $true )
& ( notdallE = $true )
& ( nonemptyI1 = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( setukpairinjL = $true )
& ( setukpairinjR1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( prop2set2propI = $true )
& ( setminusILneg = $true )
& ( symdiffI1 = $true )
& ( subsetRefl = $true )
& ( descrp = $true )
& ( setukpairinjR12 = $true )
& ( setunionsingleton2 = $true )
& ( binunionIL = $true )
& ( setukpairinjR = $true )
& ( setadjoinAx = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR2 = $true )
& ( ubforcartprodlem1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset1 = $true )
& ( cartprodpairmemER = $true )
& ( emptyinPowerset = $true )
& ( omegaIndAx = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton = $true )
& ( setunionAx = $true )
& ( exuEu = $true )
& ( subsetemptysetimpeq = $true )
& ( exu__Cong = $true )
& ( upairset2IR = $true )
& ( cartprodpairin = $true )
& ( cartprodpairmemEL = $true )
& ( setminusLsub = $true )
& ( ksndsingleton = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( ubforcartprodlem2 = $true )
& ( cartprodsndpairEq = $true )
& ( nonemptyI = $true )
& ( exuI1 = $true )
& ( powerset__Cong = $true )
& ( notinemptyset = $true )
& ( prop2setE = $true )
& ( wellorderingAx = $true )
& ( omega0Ax = $true ) ),
inference(flattening,[],[f639]) ).
thf(f678,plain,
( ( cartprodmempair = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
!= $true )
| ( $true
= ( iskpair @ X1 ) ) ) ),
inference(ennf_transformation,[],[f415]) ).
thf(f743,plain,
( ( kpairsurjEq = $true )
<=> ! [X0: $i] :
( ( ( iskpair @ X0 )
!= $true )
| ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ) ),
inference(ennf_transformation,[],[f327]) ).
thf(f889,plain,
( ( ( cartprodmempair = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true )
& ( $true
!= ( iskpair @ X1 ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
!= $true )
| ( $true
= ( iskpair @ X1 ) ) )
| ( cartprodmempair != $true ) ) ),
inference(nnf_transformation,[],[f678]) ).
thf(f890,plain,
( ( ( cartprodmempair = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $true )
& ( ( iskpair @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true )
| ( $true
= ( iskpair @ X5 ) ) )
| ( cartprodmempair != $true ) ) ),
inference(rectify,[],[f889]) ).
thf(f891,plain,
( ( ( cartprodmempair = $true )
| ( ( ( in @ sK115 @ ( cartprod @ sK114 @ sK113 ) )
= $true )
& ( $true
!= ( iskpair @ sK115 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true )
| ( $true
= ( iskpair @ X5 ) ) )
| ( cartprodmempair != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113,sK114,sK115]),skolemize(X0,sK113),skolemize(X1,sK114),skolemize(X2,sK115)],[f890]) ).
thf(f986,plain,
( ( ( kpairsurjEq = $true )
| ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 ) ) )
& ( ! [X0: $i] :
( ( ( iskpair @ X0 )
!= $true )
| ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) )
| ( kpairsurjEq != $true ) ) ),
inference(nnf_transformation,[],[f743]) ).
thf(f987,plain,
( ( ( kpairsurjEq = $true )
| ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 ) ) )
& ( ! [X1: $i] :
( ( $true
!= ( iskpair @ X1 ) )
| ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
= X1 ) )
| ( kpairsurjEq != $true ) ) ),
inference(rectify,[],[f986]) ).
thf(f988,plain,
( ( ( kpairsurjEq = $true )
| ( ( ( iskpair @ sK207 )
= $true )
& ( ( kpair @ ( kfst @ sK207 ) @ ( ksnd @ sK207 ) )
!= sK207 ) ) )
& ( ! [X1: $i] :
( ( $true
!= ( iskpair @ X1 ) )
| ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
= X1 ) )
| ( kpairsurjEq != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(X0,sK207)],[f987]) ).
thf(f1111,plain,
( ( binintersectSubset3 = $true )
& ( emptyI = $true )
& ( setunionI = $true )
& ( kfstsingleton = $true )
& ( setukpairIL = $true )
& ( singletonsubset = $true )
& ( inPowerset = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( setminusSubset2 = $true )
& ( binunionIR = $true )
& ( setukpairinjL2 = $true )
& ( setunionE = $true )
& ( emptysetsubset = $true )
& ( exuE1 = $true )
& ( subsetI2 = $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset1 = $true )
& ( theprop = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
& ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 ) )
& ( setadjoin__Cong = $true )
& ( upairsetE = $true )
& ( subsetTrans = $true )
& ( setbeta = $true )
& ( prop2setI = $true )
& ( notsubsetI = $true )
& ( binintersectI = $true )
& ( setextsub = $true )
& ( vacuousDall = $true )
& ( replAx = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem3 = $true )
& ( ex1I = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjR11 = $true )
& ( upairsubunion = $true )
& ( setminusERneg = $true )
& ( exuE3u = $true )
& ( setminusI = $true )
& ( notinsingleton = $true )
& ( binintersectEL = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( binunionLsub = $true )
& ( symdiffIneg1 = $true )
& ( emptyinunitempty = $true )
& ( inCongP = $true )
& ( singletonsuniq = $true )
& ( singletoninpowerset = $true )
& ( exuI3 = $true )
& ( ex1E1 = $true )
& ( subsetE2 = $true )
& ( disjointsetsI1 = $true )
& ( subset2powerset = $true )
& ( ex1I2 = $true )
& ( kfstpairEq = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodfstpairEq = $true )
& ( setadjoinIL = $true )
& ( symdiffE = $true )
& ( emptyE1 = $true )
& ( cartprodsndin = $true )
& ( setunionsingleton1 = $true )
& ( eqimpsubset1 = $true )
& ( uniqinunit = $true )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( sepSubset = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( notequalI2 = $true )
& ( binunionE = $true )
& ( quantDeMorgan1 = $true )
& ( singletonprop = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrEL = $true )
& ( binunionRsub = $true )
& ( setadjoinIR = $true )
& ( kpairiskpair = $true )
& ( upairset2E = $true )
& ( binintersectSubset4 = $true )
& ( singletonsswitch = $true )
& ( upairinpowunion = $true )
& ( secondinupair = $true )
& ( setminusER = $true )
& ( symdiffIneg2 = $true )
& ( subsetE = $true )
& ( binintersectSubset2 = $true )
& ( dsetconstrER = $true )
& ( setminusIRneg = $true )
& ( symdiffI2 = $true )
& ( notdexE = $true )
& ( exuE2 = $true )
& ( binintersectER = $true )
& ( bs114d = $true )
& ( upairequniteq = $true )
& ( binintersectSubset5 = $true )
& ( kpairp = $true )
& ( powersetsubset = $true )
& ( binintersectRsub = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( cartprodfstin = $true )
& ( exuI2 = $true )
& ( in__Cong = $true )
& ( omega__Cong = $true )
& ( setukpairIR = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairinjL1 = $true )
& ( noeltsimpempty = $true )
& ( setunion__Cong = $true )
& ( binunionEcases = $true )
& ( subsetI1 = $true )
& ( descr__Cong = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstr__Cong = $true )
& ( powersetI1 = $true )
& ( notequalI1 = $true )
& ( setunionE2 = $true )
& ( setminusELneg = $true )
& ( setadjoinSub = $true )
& ( setextAx = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetE = $true )
& ( ksndpairEq = $true )
& ( kpairsurjEq = $true )
& ( notdallE = $true )
& ( nonemptyI1 = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( setukpairinjL = $true )
& ( setukpairinjR1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( prop2set2propI = $true )
& ( setminusILneg = $true )
& ( symdiffI1 = $true )
& ( subsetRefl = $true )
& ( descrp = $true )
& ( setukpairinjR12 = $true )
& ( setunionsingleton2 = $true )
& ( binunionIL = $true )
& ( setukpairinjR = $true )
& ( setadjoinAx = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR2 = $true )
& ( ubforcartprodlem1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset1 = $true )
& ( cartprodpairmemER = $true )
& ( emptyinPowerset = $true )
& ( omegaIndAx = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton = $true )
& ( setunionAx = $true )
& ( exuEu = $true )
& ( subsetemptysetimpeq = $true )
& ( exu__Cong = $true )
& ( upairset2IR = $true )
& ( cartprodpairin = $true )
& ( cartprodpairmemEL = $true )
& ( setminusLsub = $true )
& ( ksndsingleton = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( ubforcartprodlem2 = $true )
& ( cartprodsndpairEq = $true )
& ( nonemptyI = $true )
& ( exuI1 = $true )
& ( powerset__Cong = $true )
& ( notinemptyset = $true )
& ( prop2setE = $true )
& ( wellorderingAx = $true )
& ( omega0Ax = $true ) ),
inference(rectify,[],[f640]) ).
thf(f1112,plain,
( ( binintersectSubset3 = $true )
& ( emptyI = $true )
& ( setunionI = $true )
& ( kfstsingleton = $true )
& ( setukpairIL = $true )
& ( singletonsubset = $true )
& ( inPowerset = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( setminusSubset2 = $true )
& ( binunionIR = $true )
& ( setukpairinjL2 = $true )
& ( setunionE = $true )
& ( emptysetsubset = $true )
& ( exuE1 = $true )
& ( subsetI2 = $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset1 = $true )
& ( theprop = $true )
& ( ( in @ sK336 @ ( cartprod @ sK337 @ sK338 ) )
= $true )
& ( sK336
!= ( kpair @ ( kfst @ sK336 ) @ ( ksnd @ sK336 ) ) )
& ( setadjoin__Cong = $true )
& ( upairsetE = $true )
& ( subsetTrans = $true )
& ( setbeta = $true )
& ( prop2setI = $true )
& ( notsubsetI = $true )
& ( binintersectI = $true )
& ( setextsub = $true )
& ( vacuousDall = $true )
& ( replAx = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem3 = $true )
& ( ex1I = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjR11 = $true )
& ( upairsubunion = $true )
& ( setminusERneg = $true )
& ( exuE3u = $true )
& ( setminusI = $true )
& ( notinsingleton = $true )
& ( binintersectEL = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( binunionLsub = $true )
& ( symdiffIneg1 = $true )
& ( emptyinunitempty = $true )
& ( inCongP = $true )
& ( singletonsuniq = $true )
& ( singletoninpowerset = $true )
& ( exuI3 = $true )
& ( ex1E1 = $true )
& ( subsetE2 = $true )
& ( disjointsetsI1 = $true )
& ( subset2powerset = $true )
& ( ex1I2 = $true )
& ( kfstpairEq = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodfstpairEq = $true )
& ( setadjoinIL = $true )
& ( symdiffE = $true )
& ( emptyE1 = $true )
& ( cartprodsndin = $true )
& ( setunionsingleton1 = $true )
& ( eqimpsubset1 = $true )
& ( uniqinunit = $true )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( sepSubset = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( notequalI2 = $true )
& ( binunionE = $true )
& ( quantDeMorgan1 = $true )
& ( singletonprop = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrEL = $true )
& ( binunionRsub = $true )
& ( setadjoinIR = $true )
& ( kpairiskpair = $true )
& ( upairset2E = $true )
& ( binintersectSubset4 = $true )
& ( singletonsswitch = $true )
& ( upairinpowunion = $true )
& ( secondinupair = $true )
& ( setminusER = $true )
& ( symdiffIneg2 = $true )
& ( subsetE = $true )
& ( binintersectSubset2 = $true )
& ( dsetconstrER = $true )
& ( setminusIRneg = $true )
& ( symdiffI2 = $true )
& ( notdexE = $true )
& ( exuE2 = $true )
& ( binintersectER = $true )
& ( bs114d = $true )
& ( upairequniteq = $true )
& ( binintersectSubset5 = $true )
& ( kpairp = $true )
& ( powersetsubset = $true )
& ( binintersectRsub = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( cartprodfstin = $true )
& ( exuI2 = $true )
& ( in__Cong = $true )
& ( omega__Cong = $true )
& ( setukpairIR = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairinjL1 = $true )
& ( noeltsimpempty = $true )
& ( setunion__Cong = $true )
& ( binunionEcases = $true )
& ( subsetI1 = $true )
& ( descr__Cong = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstr__Cong = $true )
& ( powersetI1 = $true )
& ( notequalI1 = $true )
& ( setunionE2 = $true )
& ( setminusELneg = $true )
& ( setadjoinSub = $true )
& ( setextAx = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetE = $true )
& ( ksndpairEq = $true )
& ( kpairsurjEq = $true )
& ( notdallE = $true )
& ( nonemptyI1 = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( setukpairinjL = $true )
& ( setukpairinjR1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( prop2set2propI = $true )
& ( setminusILneg = $true )
& ( symdiffI1 = $true )
& ( subsetRefl = $true )
& ( descrp = $true )
& ( setukpairinjR12 = $true )
& ( setunionsingleton2 = $true )
& ( binunionIL = $true )
& ( setukpairinjR = $true )
& ( setadjoinAx = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR2 = $true )
& ( ubforcartprodlem1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset1 = $true )
& ( cartprodpairmemER = $true )
& ( emptyinPowerset = $true )
& ( omegaIndAx = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton = $true )
& ( setunionAx = $true )
& ( exuEu = $true )
& ( subsetemptysetimpeq = $true )
& ( exu__Cong = $true )
& ( upairset2IR = $true )
& ( cartprodpairin = $true )
& ( cartprodpairmemEL = $true )
& ( setminusLsub = $true )
& ( ksndsingleton = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( ubforcartprodlem2 = $true )
& ( cartprodsndpairEq = $true )
& ( nonemptyI = $true )
& ( exuI1 = $true )
& ( powerset__Cong = $true )
& ( notinemptyset = $true )
& ( prop2setE = $true )
& ( wellorderingAx = $true )
& ( omega0Ax = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK336,sK337,sK338]),skolemize(X0,sK336),skolemize(X1,sK337),skolemize(X2,sK338)],[f1111]) ).
thf(f1457,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( cartprodmempair != $true )
| ( $true
= ( iskpair @ X5 ) )
| ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true ) ),
inference(cnf_transformation,[],[f891]) ).
thf(f1580,plain,
! [X1: $i] :
( ( kpairsurjEq != $true )
| ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
= X1 )
| ( $true
!= ( iskpair @ X1 ) ) ),
inference(cnf_transformation,[],[f988]) ).
thf(f1781,plain,
cartprodmempair = $true,
inference(cnf_transformation,[],[f1112]) ).
thf(f1821,plain,
kpairsurjEq = $true,
inference(cnf_transformation,[],[f1112]) ).
thf(f1932,plain,
( sK336
!= ( kpair @ ( kfst @ sK336 ) @ ( ksnd @ sK336 ) ) ),
inference(cnf_transformation,[],[f1112]) ).
thf(f1933,plain,
( ( in @ sK336 @ ( cartprod @ sK337 @ sK338 ) )
= $true ),
inference(cnf_transformation,[],[f1112]) ).
thf(f3298,definition,
( spl504_209
<=> ( sK336
= ( kpair @ ( kfst @ sK336 ) @ ( ksnd @ sK336 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl504_209])],[avatar_definition]) ).
thf(f3300,plain,
( ( sK336
!= ( kpair @ ( kfst @ sK336 ) @ ( ksnd @ sK336 ) ) )
| spl504_209 ),
inference(avatar_component_clause,[],[f3298]) ).
thf(f3301,plain,
~ spl504_209,
inference(avatar_split_clause,[],[f1932,f3298]) ).
thf(f3491,definition,
( spl504_253
<=> ( kpairsurjEq = $true ) ),
introduced(definition,[new_symbols(definition,[spl504_253])],[avatar_definition]) ).
thf(f3972,definition,
( spl504_359
<=> ! [X1: $i] :
( ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
= X1 )
| ( $true
!= ( iskpair @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl504_359])],[avatar_definition]) ).
thf(f3973,plain,
( ! [X1: $i] :
( ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
= X1 )
| ( $true
!= ( iskpair @ X1 ) ) )
| ~ spl504_359 ),
inference(avatar_component_clause,[],[f3972]) ).
thf(f3974,plain,
( spl504_359
| ~ spl504_253 ),
inference(avatar_split_clause,[],[f1580,f3491,f3972]) ).
thf(f4082,definition,
( spl504_383
<=> ( cartprodmempair = $true ) ),
introduced(definition,[new_symbols(definition,[spl504_383])],[avatar_definition]) ).
thf(f4873,definition,
( spl504_550
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
= ( iskpair @ X5 ) )
| ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl504_550])],[avatar_definition]) ).
thf(f4874,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true )
| ( $true
= ( iskpair @ X5 ) ) )
| ~ spl504_550 ),
inference(avatar_component_clause,[],[f4873]) ).
thf(f4875,plain,
( spl504_550
| ~ spl504_383 ),
inference(avatar_split_clause,[],[f1457,f4082,f4873]) ).
thf(f5648,definition,
( spl504_708
<=> ( ( in @ sK336 @ ( cartprod @ sK337 @ sK338 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl504_708])],[avatar_definition]) ).
thf(f5650,plain,
( ( ( in @ sK336 @ ( cartprod @ sK337 @ sK338 ) )
= $true )
| ~ spl504_708 ),
inference(avatar_component_clause,[],[f5648]) ).
thf(f5651,plain,
spl504_708,
inference(avatar_split_clause,[],[f1933,f5648]) ).
thf(f5739,plain,
spl504_383,
inference(avatar_split_clause,[],[f1781,f4082]) ).
thf(f5878,plain,
spl504_253,
inference(avatar_split_clause,[],[f1821,f3491]) ).
thf(f6631,plain,
( ( sK336 != sK336 )
| ( ( iskpair @ sK336 )
!= $true )
| spl504_209
| ~ spl504_359 ),
inference(superposition,[],[f3300,f3973]) ).
thf(f6637,plain,
( ( ( iskpair @ sK336 )
!= $true )
| spl504_209
| ~ spl504_359 ),
inference(trivial_inequality_removal,[],[f6631]) ).
thf(f6640,definition,
( spl504_835
<=> ( ( iskpair @ sK336 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl504_835])],[avatar_definition]) ).
thf(f6642,plain,
( ( ( iskpair @ sK336 )
!= $true )
| spl504_835 ),
inference(avatar_component_clause,[],[f6640]) ).
thf(f6643,plain,
( ~ spl504_835
| spl504_209
| ~ spl504_359 ),
inference(avatar_split_clause,[],[f6637,f3972,f3298,f6640]) ).
thf(f6687,plain,
( ( ( iskpair @ sK336 )
= $true )
| ( $true != $true )
| ~ spl504_550
| ~ spl504_708 ),
inference(superposition,[],[f4874,f5650]) ).
thf(f6698,plain,
( ( ( iskpair @ sK336 )
= $true )
| ~ spl504_550
| ~ spl504_708 ),
inference(trivial_inequality_removal,[],[f6687]) ).
thf(f6699,plain,
( $false
| ~ spl504_550
| ~ spl504_708
| spl504_835 ),
inference(forward_subsumption_resolution,[],[f6698,f6642]) ).
thf(f6700,plain,
( ~ spl504_550
| ~ spl504_708
| spl504_835 ),
inference(avatar_contradiction_clause,[],[f6699]) ).
cnf(s135,plain,
~ spl504_209,
inference(sat_conversion,[],[f3301]) ).
cnf(s261,plain,
( ~ spl504_253
| spl504_359 ),
inference(sat_conversion,[],[f3974]) ).
cnf(s467,plain,
( ~ spl504_383
| spl504_550 ),
inference(sat_conversion,[],[f4875]) ).
cnf(s684,plain,
spl504_708,
inference(sat_conversion,[],[f5651]) ).
cnf(s711,plain,
spl504_383,
inference(sat_conversion,[],[f5739]) ).
cnf(s744,plain,
spl504_253,
inference(sat_conversion,[],[f5878]) ).
cnf(s860,plain,
( spl504_209
| ~ spl504_359
| ~ spl504_835 ),
inference(sat_conversion,[],[f6643]) ).
cnf(s861,plain,
( ~ spl504_550
| ~ spl504_708
| spl504_835 ),
inference(sat_conversion,[],[f6700]) ).
cnf(s918,plain,
spl504_550,
inference(rat,[],[s467,s711]) ).
cnf(s919,plain,
spl504_835,
inference(rat,[],[s861,s684,s918]) ).
cnf(s972,plain,
spl504_359,
inference(rat,[],[s261,s744]) ).
cnf(s973,plain,
spl504_209,
inference(rat,[],[s860,s919,s972]) ).
cnf(s1034,plain,
$false,
inference(rat,[],[s135,s973]) ).
thf(f6701,plain,
$false,
inference(avatar_sat_refutation,[],[s1034]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU664^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:59:38 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.19/0.27 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
% 0.53/0.40 % (388435)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.53/0.40 % (388445)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2697685757:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.53/0.40 % (388446)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.53/0.40 % (388446)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
% 0.53/0.40 % (388440)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2411468132:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.53/0.40 % (388441)lrs+10_16_si=on:nwc=1.5:random_seed=2635140568:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.53/0.40 % (388442)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4242066411:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.53/0.40 % (388444)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3210940949:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.53/0.40 % (388443)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=714406418: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)
% 0.53/0.40 % (388446)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=689867702:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.53/0.40 % (388442)Instruction limit reached!
% 0.53/0.40 % (388442)------------------------------
% 0.53/0.40 % (388442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.40 % (388442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.40 % (388442)CaDiCaL version: 2.1.3
% 0.53/0.40 % (388442)Termination reason: Instruction limit
% 0.53/0.40 % (388442)Termination phase: shuffling
% 0.53/0.40 % (388442)Time elapsed: 0.002 s
% 0.53/0.40 % (388442)Peak memory usage: 10 MB
% 0.53/0.40 % (388442)Instructions burned: 3 (million)
% 0.53/0.40 % (388445)Instruction limit reached!
% 0.53/0.40 % (388445)------------------------------
% 0.53/0.40 % (388445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.40 % (388445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.40 % (388445)CaDiCaL version: 2.1.3
% 0.53/0.40 % (388445)Termination reason: Instruction limit
% 0.53/0.40 % (388445)Termination phase: Property scanning
% 0.53/0.40 % (388445)Time elapsed: 0.019 s
% 0.53/0.40 % (388445)Peak memory usage: 12 MB
% 0.53/0.40 % (388445)Instructions burned: 79 (million)
% 0.53/0.40 % (388441)Instruction limit reached!
% 0.53/0.40 % (388441)------------------------------
% 0.53/0.40 % (388441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.40 % (388441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.40 % (388441)CaDiCaL version: 2.1.3
% 0.53/0.40 % (388441)Termination reason: Instruction limit
% 0.53/0.40 % (388441)Termination phase: Property scanning
% 0.53/0.40 % (388441)Time elapsed: 0.012 s
% 0.53/0.40 % (388441)Peak memory usage: 10 MB
% 0.53/0.40 % (388441)Instructions burned: 23 (million)
% 0.53/0.40 % (388444)Instruction limit reached!
% 0.53/0.40 % (388444)------------------------------
% 0.53/0.40 % (388444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.40 % (388444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.40 % (388444)CaDiCaL version: 2.1.3
% 0.53/0.40 % (388444)Termination reason: Instruction limit
% 0.53/0.40 % (388444)Termination phase: Preprocessing 2
% 0.53/0.40 % (388444)Time elapsed: 0.011 s
% 0.53/0.40 % (388444)Peak memory usage: 11 MB
% 0.53/0.40 % (388444)Instructions burned: 25 (million)
% 0.53/0.40 % (388454)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1214552991:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.53/0.40 % (388455)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=44282060:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.53/0.40 % (388454)Instruction limit reached!
% 0.53/0.44 % (388454)------------------------------
% 0.53/0.44 % (388454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388454)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388454)Termination reason: Instruction limit
% 0.53/0.44 % (388454)Termination phase: shuffling
% 0.53/0.44 % (388454)Time elapsed: 0.001 s
% 0.53/0.44 % (388454)Peak memory usage: 10 MB
% 0.53/0.44 % (388454)Instructions burned: 2 (million)
% 0.53/0.44 % (388455)Instruction limit reached!
% 0.53/0.44 % (388455)------------------------------
% 0.53/0.44 % (388455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388455)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388455)Termination reason: Instruction limit
% 0.53/0.44 % (388455)Termination phase: shuffling
% 0.53/0.44 % (388455)Time elapsed: 0.002 s
% 0.53/0.44 % (388455)Peak memory usage: 10 MB
% 0.53/0.44 % (388455)Instructions burned: 7 (million)
% 0.53/0.44 % (388456)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.44 % (388456)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1815032176:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.53/0.44 % (388457)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=581251043:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.53/0.44 % (388461)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3352277883:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.53/0.44 % (388456)Instruction limit reached!
% 0.53/0.44 % (388456)------------------------------
% 0.53/0.44 % (388456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388456)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388456)Termination reason: Instruction limit
% 0.53/0.44 % (388456)Termination phase: shuffling
% 0.53/0.44 % (388456)Time elapsed: 0.004 s
% 0.53/0.44 % (388456)Peak memory usage: 10 MB
% 0.53/0.44 % (388456)Instructions burned: 9 (million)
% 0.53/0.44 % (388457)Instruction limit reached!
% 0.53/0.44 % (388457)------------------------------
% 0.53/0.44 % (388457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388457)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388457)Termination reason: Instruction limit
% 0.53/0.44 % (388457)Termination phase: shuffling
% 0.53/0.44 % (388457)Time elapsed: 0.006 s
% 0.53/0.44 % (388457)Peak memory usage: 10 MB
% 0.53/0.44 % (388457)Instructions burned: 13 (million)
% 0.53/0.44 % (388460)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
% 0.53/0.44 % (388460)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.44 % (388440)Instruction limit reached!
% 0.53/0.44 % (388440)------------------------------
% 0.53/0.44 % (388440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388440)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388440)Termination reason: Instruction limit
% 0.53/0.44 % (388440)Termination phase: Property scanning
% 0.53/0.44 % (388440)Time elapsed: 0.040 s
% 0.53/0.44 % (388440)Peak memory usage: 13 MB
% 0.53/0.44 % (388440)Instructions burned: 89 (million)
% 0.53/0.44 % (388460)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2150944375:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.53/0.44 % (388466)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.53/0.44 % (388461)Instruction limit reached!
% 0.53/0.44 % (388461)------------------------------
% 0.53/0.44 % (388461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388461)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388461)Termination reason: Instruction limit
% 0.53/0.44 % (388461)Termination phase: Saturation
% 0.53/0.44 % (388461)Time elapsed: 0.019 s
% 0.53/0.44 % (388461)Peak memory usage: 12 MB
% 0.53/0.44 % (388461)Instructions burned: 87 (million)
% 0.53/0.44 % (388465)lrs+10_1_si=on:cs=on:random_seed=2353927628:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.53/0.44 % (388460)Instruction limit reached!
% 0.53/0.44 % (388460)------------------------------
% 0.53/0.44 % (388460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388460)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388460)Termination reason: Instruction limit
% 0.53/0.44 % (388460)Termination phase: Property scanning
% 0.53/0.44 % (388460)Time elapsed: 0.013 s
% 0.53/0.44 % (388460)Peak memory usage: 10 MB
% 0.53/0.44 % (388460)Instructions burned: 30 (million)
% 0.53/0.44 % (388466)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=103608533:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.53/0.44 % (388467)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3830816385:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.53/0.44 % (388466)Instruction limit reached!
% 0.53/0.44 % (388466)------------------------------
% 0.53/0.44 % (388466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388466)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388466)Termination reason: Instruction limit
% 0.53/0.44 % (388466)Termination phase: shuffling
% 0.53/0.44 % (388466)Time elapsed: 0.002 s
% 0.53/0.44 % (388466)Peak memory usage: 10 MB
% 0.53/0.44 % (388466)Instructions burned: 4 (million)
% 0.53/0.44 % (388465)Instruction limit reached!
% 0.53/0.44 % (388465)------------------------------
% 0.53/0.44 % (388465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388465)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388465)Termination reason: Instruction limit
% 0.53/0.44 % (388465)Termination phase: shuffling
% 0.53/0.44 % (388465)Time elapsed: 0.004 s
% 0.53/0.44 % (388465)Peak memory usage: 10 MB
% 0.53/0.44 % (388465)Instructions burned: 9 (million)
% 0.53/0.44 % (388469)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3219097294:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.53/0.44 % (388446)Instruction limit reached!
% 0.53/0.44 % (388446)------------------------------
% 0.53/0.44 % (388446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388446)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388446)Termination reason: Instruction limit
% 0.53/0.44 % (388446)Termination phase: Saturation
% 0.53/0.44 % (388446)Time elapsed: 0.067 s
% 0.53/0.44 % (388446)Peak memory usage: 14 MB
% 0.53/0.44 % (388446)Instructions burned: 157 (million)
% 0.53/0.44 % (388472)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3094308014:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.53/0.44 % (388467)Instruction limit reached!
% 0.53/0.44 % (388467)------------------------------
% 0.53/0.44 % (388467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388467)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388467)Termination reason: Instruction limit
% 0.53/0.44 % (388467)Termination phase: Preprocessing 3
% 0.53/0.44 % (388467)Time elapsed: 0.018 s
% 0.53/0.44 % (388467)Peak memory usage: 11 MB
% 0.53/0.44 % (388467)Instructions burned: 39 (million)
% 0.53/0.44 % (388474)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=46451332:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.53/0.44 % (388475)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1725116381:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.53/0.44 % (388474)Instruction limit reached!
% 0.53/0.44 % (388474)------------------------------
% 0.53/0.44 % (388474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388474)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388474)Termination reason: Instruction limit
% 0.53/0.44 % (388474)Termination phase: shuffling
% 0.53/0.44 % (388474)Time elapsed: 0.007 s
% 0.53/0.44 % (388474)Peak memory usage: 10 MB
% 0.53/0.44 % (388474)Instructions burned: 16 (million)
% 0.53/0.44 % (388477)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2853327890:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.53/0.44 % (388472)Instruction limit reached!
% 0.53/0.44 % (388472)------------------------------
% 0.53/0.44 % (388472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388472)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388472)Termination reason: Instruction limit
% 0.53/0.44 % (388472)Termination phase: SInE selection
% 0.53/0.44 % (388472)Time elapsed: 0.012 s
% 0.53/0.44 % (388472)Peak memory usage: 11 MB
% 0.53/0.44 % (388472)Instructions burned: 27 (million)
% 0.53/0.44 % (388477)Instruction limit reached!
% 0.53/0.44 % (388477)------------------------------
% 0.53/0.44 % (388477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388477)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388477)Termination reason: Instruction limit
% 0.53/0.44 % (388477)Termination phase: shuffling
% 0.53/0.44 % (388477)Time elapsed: 0.007 s
% 0.53/0.44 % (388477)Peak memory usage: 10 MB
% 0.53/0.44 % (388477)Instructions burned: 16 (million)
% 0.53/0.44 % (388479)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1772565085:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.53/0.44 % (388479)Instruction limit reached!
% 0.53/0.44 % (388479)------------------------------
% 0.53/0.44 % (388479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.44 % (388479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.44 % (388479)CaDiCaL version: 2.1.3
% 0.53/0.44 % (388479)Termination reason: Instruction limit
% 0.53/0.44 % (388479)Termination phase: shuffling
% 0.53/0.44 % (388479)Time elapsed: 0.002 s
% 0.53/0.44 % (388479)Peak memory usage: 10 MB
% 0.53/0.44 % (388479)Instructions burned: 3 (million)
% 0.53/0.44 % (388482)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2451398675:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.53/0.44 % (388484)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3804059334:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.53/0.44 % (388443) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-388435-388443"...
% 0.53/0.44 % (388487)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 0.53/0.44 % (388487)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.53/0.44 % (388485)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2554121796:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.53/0.44 % (388443)...printing done.
% 0.53/0.44 % (388443)Refutation found. Thanks to Tanya!
% 0.53/0.44 % SZS status Theorem for theBenchmark
% 0.53/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.53/0.45 % (388443)------------------------------
% 0.53/0.45 % (388443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.45 % (388443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.45 % (388443)CaDiCaL version: 2.1.3
% 0.53/0.45 % (388443)Termination reason: Refutation
% 0.53/0.45 % (388443)Time elapsed: 0.113 s
% 0.53/0.45 % (388443)Peak memory usage: 17 MB
% 0.53/0.45 % (388443)Instructions burned: 222 (million)
% 0.53/0.45 % (388435)Success in time 0.16 s
% 0.53/0.45 % Vampire exiting
%------------------------------------------------------------------------------