TSTP Solution File: SYO856^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO856^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 08:50:15 EDT 2024
% Result : Theorem 49.76s 16.77s
% Output : CNFRefutation 49.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 56 ( 14 unt; 19 typ; 0 def)
% Number of atoms : 144 ( 32 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1485 ( 33 ~; 38 |; 21 &;1369 @)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1492 (1492 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 5 con; 0-5 aty)
% Number of variables : 1072 ( 932 ^ 137 !; 3 ?;1072 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c_False: $o ).
thf(decl_25,type,
c_not: $o > $o ).
thf(decl_28,type,
c_iff: $o > $o > $o ).
thf(decl_29,type,
c_In: $i > $i > $o ).
thf(decl_30,type,
c_Subq: $i > $i > $o ).
thf(decl_31,type,
c_Empty: $i ).
thf(decl_33,type,
c_Power: $i > $i ).
thf(decl_86,type,
c_Inj1: $i > $i ).
thf(decl_87,type,
c_Inj0: $i > $i ).
thf(decl_90,type,
c_setsum: $i > $i > $i ).
thf(decl_191,type,
esk1_0: ( ( $i > $i ) > ( ( $i > $i > $i ) > $i > $i ) > $i > ( $i > $i ) > $i ) > ( $i > $i > ( $i > $i ) > $i ) > $i ).
thf(decl_192,type,
esk2_0: ( $i > ( ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i ) > $i > $i ).
thf(decl_193,type,
esk3_0: ( $i > $i > $i ) > ( $i > $i ) > $i > $i > $i > $i ).
thf(decl_194,type,
esk4_0: ( ( ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i ) > $i ) > ( $i > $i ) > $i ).
thf(decl_196,type,
esk5_0: $i ).
thf(decl_204,type,
esk13_2: $i > $i > $i ).
thf(decl_236,type,
esk42_0: ( $i > $i ) > ( ( $i > $i > $i ) > $i > $i ) > $i > ( $i > $i ) > $i ).
thf(decl_237,type,
esk43_0: $i > $i > ( $i > $i ) > $i ).
thf(decl_239,type,
esk45_0: $i > $i ).
thf(ax13,axiom,
( c_not
= ( ^ [X17: $o] :
( X17
=> c_False ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(conj,conjecture,
! [X201: ( ( $i > $i ) > ( ( $i > $i > $i ) > $i > $i ) > $i > ( $i > $i ) > $i ) > ( $i > $i > ( $i > $i ) > $i ) > $i,X202: ( $i > ( ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i ) > $i > $i,X203: ( $i > $i > $i ) > ( $i > $i ) > $i > $i > $i > $i,X204: ( ( ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i ) > $i ) > ( $i > $i ) > $i] :
( ! [X205: ( $i > $i > $i ) > $i,X206: $i,X207: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i > $i,X208: ( ( $i > $i > $i ) > $i ) > ( $i > $i ) > $i > $i > $i] :
( ( X204
@ ^ [X209: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( c_setsum
@ ( X201
@ ^ [X210: $i > $i,X211: ( $i > $i > $i ) > $i > $i,X212: $i,X213: $i > $i] :
( X202
@ ^ [X214: $i,X215: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj1 @ c_Empty ) )
@ ^ [X216: $i,X217: $i,X218: $i > $i] : c_Empty )
@ ( X202
@ ^ [X219: $i,X220: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( X203
@ ^ [X221: $i,X222: $i] :
( X208
@ ^ [X169: $i > $i > $i] : c_Empty
@ ^ [X223: $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [X224: $i] : c_Empty
@ ( X207
@ ^ [X225: ( $i > $i ) > $i,X226: $i > $i,X227: $i] : c_Empty
@ c_Empty )
@ ( X202
@ ^ [X228: $i,X229: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty )
@ ( c_Inj0 @ c_Empty ) ) ) )
@ ^ [X230: $i] : X230 )
= ( c_Inj1 @ c_Empty ) )
=> ( ! [X66: $i,X231: $i,X232: $i > $i,X233: $i] :
( ( X204
@ ^ [X234: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [X235: $i] : ( X232 @ X235 ) )
= ( X232
@ ( c_setsum
@ ( X203
@ ^ [X236: $i,X237: $i] :
( X202
@ ^ [X238: $i,X239: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [X240: $i] : X240
@ X231
@ c_Empty
@ c_Empty )
@ ( X202
@ ^ [X241: $i,X242: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X242
@ ^ [X243: $i > $i,X244: $i] : c_Empty
@ X241
@ ( X203
@ ^ [X245: $i,X246: $i] : c_Empty
@ ^ [X247: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) )
@ c_Empty ) ) ) )
=> ( ! [X66: $i,X248: ( $i > ( $i > $i ) > $i ) > $i,X83: $i,X249: $i > $i] :
( ( X203
@ ^ [X250: $i,X251: $i] : c_Empty
@ ^ [X252: $i] :
( X203
@ ^ [X253: $i,X254: $i] :
( X203
@ ^ [X255: $i,X256: $i] : c_Empty
@ ^ [X257: $i] : c_Empty
@ ( X201
@ ^ [X258: $i > $i,X259: ( $i > $i > $i ) > $i > $i,X260: $i,X261: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [X262: $i,X263: $i,X264: $i > $i] :
( X201
@ ^ [X265: $i > $i,X266: ( $i > $i > $i ) > $i > $i,X174: $i,X267: $i > $i] : c_Empty
@ ^ [X172: $i,X173: $i,X268: $i > $i] : c_Empty ) )
@ ( X249 @ X254 )
@ X254 )
@ ^ [X269: $i] : X252
@ ( X202
@ ^ [X270: $i,X271: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( X203
@ ^ [X272: $i,X273: $i] : ( c_Inj1 @ c_Empty )
@ ^ [X274: $i] :
( X202
@ ^ [X275: $i,X276: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty )
@ ( X204
@ ^ [X277: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [X278: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty )
@ ( X201
@ ^ [X279: $i > $i,X280: ( $i > $i > $i ) > $i > $i,X281: $i,X282: $i > $i] : c_Empty
@ ^ [X283: $i,X284: $i,X285: $i > $i] : c_Empty ) ) )
@ ( X249 @ c_Empty )
@ c_Empty )
@ X66
@ ( X201
@ ^ [X286: $i > $i,X287: ( $i > $i > $i ) > $i > $i,X288: $i,X289: $i > $i] : ( c_Inj0 @ c_Empty )
@ ^ [X290: $i,X291: $i,X292: $i > $i] :
( c_Inj0
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( X202
@ ^ [X293: $i,X294: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum @ c_Empty @ ( X249 @ c_Empty ) ) )
= X66 )
=> ( ! [X295: $i > $i > $i,X296: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i > $i > $i > $i,X297: ( ( $i > $i > $i ) > $i > $i ) > $i,X298: $i > $i] :
( ( X203
@ ^ [X299: $i,X300: $i] :
( X203
@ ^ [X301: $i,X302: $i] : c_Empty
@ ^ [X303: $i] : X299
@ ( X298 @ c_Empty )
@ ( X297
@ ^ [X168: $i > $i > $i,X304: $i] :
( c_setsum @ c_Empty
@ ( X201
@ ^ [X305: $i > $i,X306: ( $i > $i > $i ) > $i > $i,X172: $i,X307: $i > $i] : c_Empty
@ ^ [X308: $i,X309: $i,X310: $i > $i] : c_Empty ) ) )
@ c_Empty )
@ ^ [X311: $i] : c_Empty
@ ( X296
@ ^ [X312: ( $i > $i ) > $i,X313: $i > $i,X314: $i] : c_Empty
@ c_Empty
@ ( X203
@ ^ [X315: $i,X316: $i] :
( X204
@ ^ [X317: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : X316
@ ^ [X318: $i] : ( c_Inj0 @ c_Empty ) )
@ ^ [X319: $i] :
( X204
@ ^ [X320: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( X297
@ ^ [X168: $i > $i > $i,X321: $i] : c_Empty )
@ ^ [X322: $i] : ( c_Inj0 @ c_Empty ) )
@ ( X298 @ c_Empty )
@ c_Empty
@ ( X296
@ ^ [X323: ( $i > $i ) > $i,X324: $i > $i,X325: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj1 @ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ c_Empty ) )
@ ( c_Inj0 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( X298 @ c_Empty ) ) ) )
@ ( c_Inj1
@ ( c_setsum @ c_Empty
@ ( X296
@ ^ [X326: ( $i > $i ) > $i,X327: $i > $i,X328: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ c_Empty
@ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( X298 @ ( c_Inj1 @ c_Empty ) ) )
= ( X298 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ! [X66: $i,X329: $i > $i > ( $i > $i ) > $i > $i,X330: ( ( $i > $i ) > $i > $i ) > $i,X331: $i] :
( ( X202
@ ^ [X332: $i,X333: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum
@ ( X203
@ ^ [X334: $i,X335: $i] : c_Empty
@ ^ [X336: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ ( X204
@ ^ [X337: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [X338: $i] : c_Empty ) ) )
@ ( c_setsum
@ ( c_setsum
@ ( X201
@ ^ [X339: $i > $i,X340: ( $i > $i > $i ) > $i > $i,X341: $i,X342: $i > $i] : c_Empty
@ ^ [X343: $i,X344: $i,X345: $i > $i] : c_Empty )
@ c_Empty )
@ ( X333
@ ^ [X346: $i > $i,X347: $i] : ( c_Inj0 @ c_Empty )
@ ( X333
@ ^ [X348: $i > $i,X349: $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) )
@ ( X203
@ ^ [X350: $i,X351: $i] : c_Empty
@ ^ [X352: $i] :
( X330
@ ^ [X353: $i > $i,X354: $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X203
@ ^ [X355: $i,X356: $i] : c_Empty
@ ^ [X357: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) )
@ ( c_setsum @ X66 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) )
= ( X203
@ ^ [X358: $i,X359: $i] : ( c_setsum @ X331 @ ( c_Inj1 @ X331 ) )
@ ^ [X360: $i] :
( X201
@ ^ [X361: $i > $i,X362: ( $i > $i > $i ) > $i > $i,X363: $i,X364: $i > $i] : ( c_Inj1 @ c_Empty )
@ ^ [X365: $i,X366: $i,X367: $i > $i] : c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( c_Inj0
@ ( X201
@ ^ [X368: $i > $i,X369: ( $i > $i > $i ) > $i > $i,X370: $i,X371: $i > $i] : ( c_Inj1 @ c_Empty )
@ ^ [X372: $i,X373: $i,X374: $i > $i] :
( c_Inj0
@ ( X203
@ ^ [X375: $i,X376: $i] : c_Empty
@ ^ [X377: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum
@ ( c_Inj1
@ ( X330
@ ^ [X378: $i > $i,X379: $i] : ( c_Inj1 @ c_Empty ) ) )
@ ( c_setsum
@ ( X204
@ ^ [X380: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( X380
@ ^ [X381: $i > $i > $i,X382: $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [X383: $i] : ( c_Inj1 @ c_Empty ) )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ! [X384: $i > ( $i > $i > $i ) > $i > $i,X385: $i,X83: $i,X386: ( ( $i > $i > $i ) > $i > $i ) > $i] :
( ( X202
@ ^ [X387: $i,X388: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( X202
@ ^ [X389: $i,X390: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : X387
@ ( c_setsum
@ ( X203
@ ^ [X391: $i,X392: $i] : c_Empty
@ ^ [X393: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ ( X202
@ ^ [X394: $i,X395: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ c_Empty )
@ ( X203
@ ^ [X396: $i,X397: $i] : X397
@ ^ [X398: $i] :
( X201
@ ^ [X399: $i > $i,X400: ( $i > $i > $i ) > $i > $i,X401: $i,X402: $i > $i] : X401
@ ^ [X403: $i,X404: $i,X405: $i > $i] :
( X204
@ ^ [X406: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( X406
@ ^ [X171: $i > $i > $i,X407: $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [X408: $i] : c_Empty ) )
@ X385
@ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ c_Empty
@ ( c_Inj1
@ ( X203
@ ^ [X409: $i,X410: $i] : c_Empty
@ ^ [X411: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) ) )
= ( X203
@ ^ [X412: $i,X413: $i] : ( c_Inj0 @ c_Empty )
@ ^ [X414: $i] :
( X202
@ ^ [X415: $i,X416: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X386
@ ^ [X169: $i > $i > $i,X417: $i] :
( X416
@ ^ [X418: $i > $i,X172: $i] :
( X203
@ ^ [X173: $i,X174: $i] : c_Empty
@ ^ [X173: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ c_Empty
@ ( X202
@ ^ [X419: $i,X420: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ c_Empty )
@ ( c_Inj0
@ ( X204
@ ^ [X421: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [X422: $i] :
( X204
@ ^ [X423: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [X424: $i] :
( X203
@ ^ [X425: $i,X426: $i] : c_Empty
@ ^ [X427: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum
@ ( c_setsum @ X385
@ ( X202
@ ^ [X428: $i,X429: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( c_Inj0 @ c_Empty )
@ ( X203
@ ^ [X430: $i,X431: $i] : c_Empty
@ ^ [X432: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) )
@ ( X202
@ ^ [X433: $i,X434: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_Inj0
@ ( X201
@ ^ [X435: $i > $i,X436: ( $i > $i > $i ) > $i > $i,X437: $i,X438: $i > $i] : c_Empty
@ ^ [X439: $i,X440: $i,X441: $i > $i] : c_Empty ) )
@ X385 ) )
@ ( c_setsum
@ ( c_setsum @ X83
@ ( X203
@ ^ [X442: $i,X443: $i] : X443
@ ^ [X444: $i] :
( X386
@ ^ [X445: $i > $i > $i,X446: $i] : c_Empty )
@ ( X384 @ c_Empty
@ ^ [X447: $i,X448: $i] : c_Empty
@ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( X204
@ ^ [X449: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [X450: $i] : c_Empty ) ) )
@ ( X384
@ ( X204
@ ^ [X451: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [X452: $i] :
( X201
@ ^ [X453: $i > $i,X454: ( $i > $i > $i ) > $i > $i,X455: $i,X456: $i > $i] : c_Empty
@ ^ [X457: $i,X458: $i,X459: $i > $i] : c_Empty ) )
@ ^ [X460: $i,X461: $i] :
( X202
@ ^ [X462: $i,X463: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X463
@ ^ [X464: $i > $i,X465: $i] : c_Empty
@ c_Empty
@ c_Empty )
@ X461 )
@ X385 ) ) ) )
=> ( ! [X466: ( $i > $i ) > $i,X82: $i > $i,X83: $i,X467: $i] :
( ( X201
@ ^ [X468: $i > $i,X469: ( $i > $i > $i ) > $i > $i,X470: $i,X471: $i > $i] : c_Empty
@ ^ [X472: $i,X473: $i,X474: $i > $i] :
( X201
@ ^ [X475: $i > $i,X476: ( $i > $i > $i ) > $i > $i,X477: $i,X478: $i > $i] :
( X203
@ ^ [X173: $i,X174: $i] : ( X478 @ X477 )
@ ^ [X173: $i] : X173
@ c_Empty
@ ( X478
@ ( X204
@ ^ [X479: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [X173: $i] : c_Empty ) )
@ ( X201
@ ^ [X480: $i > $i,X481: ( $i > $i > $i ) > $i > $i,X181: $i,X482: $i > $i] : ( c_Inj0 @ c_Empty )
@ ^ [X173: $i,X174: $i,X483: $i > $i] :
( X202
@ ^ [X188: $i,X484: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ ^ [X485: $i,X486: $i,X487: $i > $i] :
( c_Inj1
@ ( X201
@ ^ [X488: $i > $i,X489: ( $i > $i > $i ) > $i > $i,X174: $i,X490: $i > $i] : c_Empty
@ ^ [X172: $i,X173: $i,X491: $i > $i] : ( X487 @ c_Empty ) ) ) ) )
= ( X201
@ ^ [X492: $i > $i,X493: ( $i > $i > $i ) > $i > $i,X494: $i,X495: $i > $i] :
( c_setsum
@ ( X201
@ ^ [X496: $i > $i,X497: ( $i > $i > $i ) > $i > $i,X172: $i,X498: $i > $i] : c_Empty
@ ^ [X499: $i,X500: $i,X501: $i > $i] : c_Empty )
@ c_Empty )
@ ^ [X502: $i,X503: $i,X504: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) )
=> ( ! [X66: $i,X505: $i,X83: $i,X506: $i] :
( ( X201
@ ^ [X507: $i > $i,X508: ( $i > $i > $i ) > $i > $i,X509: $i,X510: $i > $i] : c_Empty
@ ^ [X511: $i,X512: $i,X513: $i > $i] : c_Empty )
= X66 )
=> c_False ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(ax5,axiom,
( c_not
@ ? [X7: $i] : ( c_In @ X7 @ c_Empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(ax17,axiom,
( c_Subq
= ( ^ [X26: $i,X2: $i] :
! [X9: $i] :
( ( c_In @ X9 @ X26 )
=> ( c_In @ X9 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(ax7,axiom,
! [X10: $i,X2: $i] : ( c_iff @ ( c_In @ X2 @ ( c_Power @ X10 ) ) @ ( c_Subq @ X2 @ X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
thf(ax3,axiom,
! [X4: $o,X5: $o] :
( ( c_iff @ X4 @ X5 )
=> ( X4
<=> X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(c_0_6,plain,
! [X578: $o] :
( ( c_not @ X578 )
<=> ( X578
=> c_False ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax13])]) ).
thf(c_0_7,negated_conjecture,
~ ! [X201: ( ( $i > $i ) > ( ( $i > $i > $i ) > $i > $i ) > $i > ( $i > $i ) > $i ) > ( $i > $i > ( $i > $i ) > $i ) > $i,X202: ( $i > ( ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i ) > $i > $i,X203: ( $i > $i > $i ) > ( $i > $i ) > $i > $i > $i > $i,X204: ( ( ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i ) > $i ) > ( $i > $i ) > $i] :
( ! [X205: ( $i > $i > $i ) > $i,X206: $i,X207: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i > $i,X208: ( ( $i > $i > $i ) > $i ) > ( $i > $i ) > $i > $i > $i] :
( ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( c_setsum
@ ( X201
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] :
( X202
@ ^ [Z5: $i,Z6: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj1 @ c_Empty ) )
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty )
@ ( X202
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( X203
@ ^ [Z1: $i,Z2: $i] :
( X208
@ ^ [Z3: $i > $i > $i] : c_Empty
@ ^ [Z3: $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [Z1: $i] : c_Empty
@ ( X207
@ ^ [Z1: ( $i > $i ) > $i,Z2: $i > $i,Z3: $i] : c_Empty
@ c_Empty )
@ ( X202
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty )
@ ( c_Inj0 @ c_Empty ) ) ) )
@ ^ [Z0: $i] : Z0 )
= ( c_Inj1 @ c_Empty ) )
=> ( ! [X66: $i,X231: $i,X232: $i > $i,X233: $i] :
( ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ X232 )
= ( X232
@ ( c_setsum
@ ( X203
@ ^ [Z0: $i,Z1: $i] :
( X202
@ ^ [Z2: $i,Z3: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [Z0: $i] : Z0
@ X231
@ c_Empty
@ c_Empty )
@ ( X202
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( Z1
@ ^ [Z2: $i > $i,Z3: $i] : c_Empty
@ Z0
@ ( X203
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) )
@ c_Empty ) ) ) )
=> ( ! [X66: $i,X248: ( $i > ( $i > $i ) > $i ) > $i,X83: $i,X249: $i > $i] :
( ( X203
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ ^ [Z0: $i] :
( X203
@ ^ [Z1: $i,Z2: $i] :
( X203
@ ^ [Z3: $i,Z4: $i] : c_Empty
@ ^ [Z3: $i] : c_Empty
@ ( X201
@ ^ [Z3: $i > $i,Z4: ( $i > $i > $i ) > $i > $i,Z5: $i,Z6: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [Z3: $i,Z4: $i,Z5: $i > $i] :
( X201
@ ^ [Z6: $i > $i,Z7: ( $i > $i > $i ) > $i > $i,Z8: $i,Z9: $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: $i,Z8: $i > $i] : c_Empty ) )
@ ( X249 @ Z2 )
@ Z2 )
@ ^ [Z1: $i] : Z0
@ ( X202
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( X203
@ ^ [Z1: $i,Z2: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Z1: $i] :
( X202
@ ^ [Z2: $i,Z3: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty )
@ ( X204
@ ^ [Z1: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty )
@ ( X201
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty ) ) )
@ ( X249 @ c_Empty )
@ c_Empty )
@ X66
@ ( X201
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] : ( c_Inj0 @ c_Empty )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( c_Inj0
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( X202
@ ^ [Z3: $i,Z4: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum @ c_Empty @ ( X249 @ c_Empty ) ) )
= X66 )
=> ( ! [X295: $i > $i > $i,X296: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i > $i > $i > $i,X297: ( ( $i > $i > $i ) > $i > $i ) > $i,X298: $i > $i] :
( ( X203
@ ^ [Z0: $i,Z1: $i] :
( X203
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : Z0
@ ( X298 @ c_Empty )
@ ( X297
@ ^ [Z2: $i > $i > $i,Z3: $i] :
( c_setsum @ c_Empty
@ ( X201
@ ^ [Z4: $i > $i,Z5: ( $i > $i > $i ) > $i > $i,Z6: $i,Z7: $i > $i] : c_Empty
@ ^ [Z4: $i,Z5: $i,Z6: $i > $i] : c_Empty ) ) )
@ c_Empty )
@ ^ [Z0: $i] : c_Empty
@ ( X296
@ ^ [Z0: ( $i > $i ) > $i,Z1: $i > $i,Z2: $i] : c_Empty
@ c_Empty
@ ( X203
@ ^ [Z0: $i,Z1: $i] :
( X204
@ ^ [Z2: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : Z1
@ ^ [Z2: $i] : ( c_Inj0 @ c_Empty ) )
@ ^ [Z0: $i] :
( X204
@ ^ [Z1: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( X297
@ ^ [Z2: $i > $i > $i,Z3: $i] : c_Empty )
@ ^ [Z1: $i] : ( c_Inj0 @ c_Empty ) )
@ ( X298 @ c_Empty )
@ c_Empty
@ ( X296
@ ^ [Z0: ( $i > $i ) > $i,Z1: $i > $i,Z2: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj1 @ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ c_Empty ) )
@ ( c_Inj0 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( X298 @ c_Empty ) ) ) )
@ ( c_Inj1
@ ( c_setsum @ c_Empty
@ ( X296
@ ^ [Z0: ( $i > $i ) > $i,Z1: $i > $i,Z2: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ c_Empty
@ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( X298 @ ( c_Inj1 @ c_Empty ) ) )
= ( X298 @ ( c_Inj0 @ c_Empty ) ) )
=> ( ! [X66: $i,X329: $i > $i > ( $i > $i ) > $i > $i,X330: ( ( $i > $i ) > $i > $i ) > $i,X331: $i] :
( ( X202
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum
@ ( X203
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ ( X204
@ ^ [Z2: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z2: $i] : c_Empty ) ) )
@ ( c_setsum
@ ( c_setsum
@ ( X201
@ ^ [Z2: $i > $i,Z3: ( $i > $i > $i ) > $i > $i,Z4: $i,Z5: $i > $i] : c_Empty
@ ^ [Z2: $i,Z3: $i,Z4: $i > $i] : c_Empty )
@ c_Empty )
@ ( Z1
@ ^ [Z2: $i > $i,Z3: $i] : ( c_Inj0 @ c_Empty )
@ ( Z1
@ ^ [Z2: $i > $i,Z3: $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) )
@ ( X203
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ ^ [Z0: $i] :
( X330
@ ^ [Z1: $i > $i,Z2: $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X203
@ ^ [Z3: $i,Z4: $i] : c_Empty
@ ^ [Z3: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) )
@ ( c_setsum @ X66 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) )
= ( X203
@ ^ [Z0: $i,Z1: $i] : ( c_setsum @ X331 @ ( c_Inj1 @ X331 ) )
@ ^ [Z0: $i] :
( X201
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] : ( c_Inj1 @ c_Empty )
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( c_Inj0
@ ( X201
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] : ( c_Inj1 @ c_Empty )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( c_Inj0
@ ( X203
@ ^ [Z3: $i,Z4: $i] : c_Empty
@ ^ [Z3: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum
@ ( c_Inj1
@ ( X330
@ ^ [Z0: $i > $i,Z1: $i] : ( c_Inj1 @ c_Empty ) ) )
@ ( c_setsum
@ ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( Z0
@ ^ [Z1: $i > $i > $i,Z2: $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [Z0: $i] : ( c_Inj1 @ c_Empty ) )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ! [X384: $i > ( $i > $i > $i ) > $i > $i,X385: $i,X83: $i,X386: ( ( $i > $i > $i ) > $i > $i ) > $i] :
( ( X202
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( X202
@ ^ [Z2: $i,Z3: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : Z0
@ ( c_setsum
@ ( X203
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ ( X202
@ ^ [Z2: $i,Z3: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ c_Empty )
@ ( X203
@ ^ [Z0: $i,Z1: $i] : Z1
@ ^ [Z0: $i] :
( X201
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] : Z3
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] :
( X204
@ ^ [Z4: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( Z4
@ ^ [Z5: $i > $i > $i,Z6: $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [Z4: $i] : c_Empty ) )
@ X385
@ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ c_Empty
@ ( c_Inj1
@ ( X203
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ ^ [Z0: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) ) )
= ( X203
@ ^ [Z0: $i,Z1: $i] : ( c_Inj0 @ c_Empty )
@ ^ [Z0: $i] :
( X202
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X386
@ ^ [Z3: $i > $i > $i,Z4: $i] :
( Z2
@ ^ [Z5: $i > $i,Z6: $i] :
( X203
@ ^ [Z7: $i,Z8: $i] : c_Empty
@ ^ [Z7: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ c_Empty
@ ( X202
@ ^ [Z5: $i,Z6: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ c_Empty )
@ ( c_Inj0
@ ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [Z0: $i] :
( X204
@ ^ [Z1: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [Z1: $i] :
( X203
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum
@ ( c_setsum @ X385
@ ( X202
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( c_Inj0 @ c_Empty )
@ ( X203
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ ^ [Z0: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) )
@ ( X202
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_Inj0
@ ( X201
@ ^ [Z2: $i > $i,Z3: ( $i > $i > $i ) > $i > $i,Z4: $i,Z5: $i > $i] : c_Empty
@ ^ [Z2: $i,Z3: $i,Z4: $i > $i] : c_Empty ) )
@ X385 ) )
@ ( c_setsum
@ ( c_setsum @ X83
@ ( X203
@ ^ [Z0: $i,Z1: $i] : Z1
@ ^ [Z0: $i] :
( X386
@ ^ [Z1: $i > $i > $i,Z2: $i] : c_Empty )
@ ( X384 @ c_Empty
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z0: $i] : c_Empty ) ) )
@ ( X384
@ ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z0: $i] :
( X201
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty ) )
@ ^ [Z0: $i] :
( X202
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( Z2
@ ^ [Z3: $i > $i,Z4: $i] : c_Empty
@ c_Empty
@ c_Empty ) )
@ X385 ) ) ) )
=> ( ! [X466: ( $i > $i ) > $i,X82: $i > $i,X83: $i,X467: $i] :
( ( X201
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] : c_Empty
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( X201
@ ^ [Z3: $i > $i,Z4: ( $i > $i > $i ) > $i > $i,Z5: $i,Z6: $i > $i] :
( X203
@ ^ [Z7: $i,Z8: $i] : ( Z6 @ Z5 )
@ ^ [Z7: $i] : Z7
@ c_Empty
@ ( Z6
@ ( X204
@ ^ [Z7: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z7: $i] : c_Empty ) )
@ ( X201
@ ^ [Z7: $i > $i,Z8: ( $i > $i > $i ) > $i > $i,Z9: $i,Z10: $i > $i] : ( c_Inj0 @ c_Empty )
@ ^ [Z7: $i,Z8: $i,Z9: $i > $i] :
( X202
@ ^ [Z10: $i,Z11: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ ^ [Z3: $i,Z4: $i,Z5: $i > $i] :
( c_Inj1
@ ( X201
@ ^ [Z6: $i > $i,Z7: ( $i > $i > $i ) > $i > $i,Z8: $i,Z9: $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: $i,Z8: $i > $i] : ( Z5 @ c_Empty ) ) ) ) )
= ( X201
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] :
( c_setsum
@ ( X201
@ ^ [Z4: $i > $i,Z5: ( $i > $i > $i ) > $i > $i,Z6: $i,Z7: $i > $i] : c_Empty
@ ^ [Z4: $i,Z5: $i,Z6: $i > $i] : c_Empty )
@ c_Empty )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) )
=> ( ! [X66: $i,X505: $i,X83: $i,X506: $i] :
( ( X201
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] : c_Empty
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] : c_Empty )
= X66 )
=> c_False ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj])])]) ).
thf(c_0_8,axiom,
( ( ~ ? [X7: $i] : ( c_In @ X7 @ c_Empty )
| ( c_not @ $true ) )
& ( ? [X7: $i] : ( c_In @ X7 @ c_Empty )
| ( c_not @ $false ) ) ),
inference(fool_unroll,[status(thm)],[ax5]) ).
thf(c_0_9,plain,
! [X701: $o] :
( ( ~ ( c_not @ X701 )
| ~ X701
| c_False )
& ( X701
| ( c_not @ X701 ) )
& ( ~ c_False
| ( c_not @ X701 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
thf(c_0_10,negated_conjecture,
! [X682: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i > $i,X683: ( ( $i > $i > $i ) > $i ) > ( $i > $i ) > $i > $i > $i,X684: $i,X685: $i > $i,X686: $i,X687: $i > $i,X688: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i > $i > $i > $i,X689: ( ( $i > $i > $i ) > $i > $i ) > $i,X690: $i > $i,X691: $i,X692: ( ( $i > $i ) > $i > $i ) > $i,X693: $i,X694: $i > ( $i > $i > $i ) > $i > $i,X695: $i,X696: $i,X697: ( ( $i > $i > $i ) > $i > $i ) > $i,X698: $i] :
( ( ( esk4_0
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( c_setsum
@ ( esk1_0
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] :
( esk2_0
@ ^ [Z5: $i,Z6: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj1 @ c_Empty ) )
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty )
@ ( esk2_0
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( esk3_0
@ ^ [Z1: $i,Z2: $i] :
( X683
@ ^ [Z3: $i > $i > $i] : c_Empty
@ ^ [Z3: $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [Z1: $i] : c_Empty
@ ( X682
@ ^ [Z1: ( $i > $i ) > $i,Z2: $i > $i,Z3: $i] : c_Empty
@ c_Empty )
@ ( esk2_0
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty )
@ ( c_Inj0 @ c_Empty ) ) ) )
@ ^ [Z0: $i] : Z0 )
= ( c_Inj1 @ c_Empty ) )
& ( ( esk4_0
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ X685 )
= ( X685
@ ( c_setsum
@ ( esk3_0
@ ^ [Z0: $i,Z1: $i] :
( esk2_0
@ ^ [Z2: $i,Z3: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [Z0: $i] : Z0
@ X684
@ c_Empty
@ c_Empty )
@ ( esk2_0
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( Z1
@ ^ [Z2: $i > $i,Z3: $i] : c_Empty
@ Z0
@ ( esk3_0
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) )
@ c_Empty ) ) ) )
& ( ( esk3_0
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ ^ [Z0: $i] :
( esk3_0
@ ^ [Z1: $i,Z2: $i] :
( esk3_0
@ ^ [Z3: $i,Z4: $i] : c_Empty
@ ^ [Z3: $i] : c_Empty
@ ( esk1_0
@ ^ [Z3: $i > $i,Z4: ( $i > $i > $i ) > $i > $i,Z5: $i,Z6: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [Z3: $i,Z4: $i,Z5: $i > $i] :
( esk1_0
@ ^ [Z6: $i > $i,Z7: ( $i > $i > $i ) > $i > $i,Z8: $i,Z9: $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: $i,Z8: $i > $i] : c_Empty ) )
@ ( X687 @ Z2 )
@ Z2 )
@ ^ [Z1: $i] : Z0
@ ( esk2_0
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ( esk3_0
@ ^ [Z1: $i,Z2: $i] : ( c_Inj1 @ c_Empty )
@ ^ [Z1: $i] :
( esk2_0
@ ^ [Z2: $i,Z3: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty )
@ ( esk4_0
@ ^ [Z1: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z1: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty )
@ ( esk1_0
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty ) ) )
@ ( X687 @ c_Empty )
@ c_Empty )
@ X686
@ ( esk1_0
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] : ( c_Inj0 @ c_Empty )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( c_Inj0
@ ( c_setsum @ ( c_Inj0 @ c_Empty )
@ ( esk2_0
@ ^ [Z3: $i,Z4: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum @ c_Empty @ ( X687 @ c_Empty ) ) )
= X686 )
& ( ( esk3_0
@ ^ [Z0: $i,Z1: $i] :
( esk3_0
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : Z0
@ ( X690 @ c_Empty )
@ ( X689
@ ^ [Z2: $i > $i > $i,Z3: $i] :
( c_setsum @ c_Empty
@ ( esk1_0
@ ^ [Z4: $i > $i,Z5: ( $i > $i > $i ) > $i > $i,Z6: $i,Z7: $i > $i] : c_Empty
@ ^ [Z4: $i,Z5: $i,Z6: $i > $i] : c_Empty ) ) )
@ c_Empty )
@ ^ [Z0: $i] : c_Empty
@ ( X688
@ ^ [Z0: ( $i > $i ) > $i,Z1: $i > $i,Z2: $i] : c_Empty
@ c_Empty
@ ( esk3_0
@ ^ [Z0: $i,Z1: $i] :
( esk4_0
@ ^ [Z2: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : Z1
@ ^ [Z2: $i] : ( c_Inj0 @ c_Empty ) )
@ ^ [Z0: $i] :
( esk4_0
@ ^ [Z1: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( X689
@ ^ [Z2: $i > $i > $i,Z3: $i] : c_Empty )
@ ^ [Z1: $i] : ( c_Inj0 @ c_Empty ) )
@ ( X690 @ c_Empty )
@ c_Empty
@ ( X688
@ ^ [Z0: ( $i > $i ) > $i,Z1: $i > $i,Z2: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( c_Inj1 @ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ c_Empty ) )
@ ( c_Inj0 @ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( X690 @ c_Empty ) ) ) )
@ ( c_Inj1
@ ( c_setsum @ c_Empty
@ ( X688
@ ^ [Z0: ( $i > $i ) > $i,Z1: $i > $i,Z2: $i] : ( c_setsum @ c_Empty @ c_Empty )
@ c_Empty
@ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( X690 @ ( c_Inj1 @ c_Empty ) ) )
= ( X690 @ ( c_Inj0 @ c_Empty ) ) )
& ( ( esk2_0
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( c_setsum
@ ( esk3_0
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ ( esk4_0
@ ^ [Z2: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z2: $i] : c_Empty ) ) )
@ ( c_setsum
@ ( c_setsum
@ ( esk1_0
@ ^ [Z2: $i > $i,Z3: ( $i > $i > $i ) > $i > $i,Z4: $i,Z5: $i > $i] : c_Empty
@ ^ [Z2: $i,Z3: $i,Z4: $i > $i] : c_Empty )
@ c_Empty )
@ ( Z1
@ ^ [Z2: $i > $i,Z3: $i] : ( c_Inj0 @ c_Empty )
@ ( Z1
@ ^ [Z2: $i > $i,Z3: $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ( c_Inj1 @ c_Empty ) ) ) )
@ ( esk3_0
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ ^ [Z0: $i] :
( X692
@ ^ [Z1: $i > $i,Z2: $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( esk3_0
@ ^ [Z3: $i,Z4: $i] : c_Empty
@ ^ [Z3: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) )
@ ( c_setsum @ X691 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ c_Empty
@ ( c_Inj0 @ c_Empty ) ) )
= ( esk3_0
@ ^ [Z0: $i,Z1: $i] : ( c_setsum @ X693 @ ( c_Inj1 @ X693 ) )
@ ^ [Z0: $i] :
( esk1_0
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] : ( c_Inj1 @ c_Empty )
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( c_Inj0
@ ( esk1_0
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] : ( c_Inj1 @ c_Empty )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( c_Inj0
@ ( esk3_0
@ ^ [Z3: $i,Z4: $i] : c_Empty
@ ^ [Z3: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum
@ ( c_Inj1
@ ( X692
@ ^ [Z0: $i > $i,Z1: $i] : ( c_Inj1 @ c_Empty ) ) )
@ ( c_setsum
@ ( esk4_0
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( Z0
@ ^ [Z1: $i > $i > $i,Z2: $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [Z0: $i] : ( c_Inj1 @ c_Empty ) )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
& ( ( esk2_0
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( esk2_0
@ ^ [Z2: $i,Z3: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : Z0
@ ( c_setsum
@ ( esk3_0
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ ( esk2_0
@ ^ [Z2: $i,Z3: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ c_Empty )
@ ( esk3_0
@ ^ [Z0: $i,Z1: $i] : Z1
@ ^ [Z0: $i] :
( esk1_0
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] : Z3
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] :
( esk4_0
@ ^ [Z4: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] :
( Z4
@ ^ [Z5: $i > $i > $i,Z6: $i > $i] : c_Empty
@ c_Empty
@ c_Empty )
@ ^ [Z4: $i] : c_Empty ) )
@ X695
@ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ c_Empty
@ ( c_Inj1
@ ( esk3_0
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ ^ [Z0: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) ) )
= ( esk3_0
@ ^ [Z0: $i,Z1: $i] : ( c_Inj0 @ c_Empty )
@ ^ [Z0: $i] :
( esk2_0
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X697
@ ^ [Z3: $i > $i > $i,Z4: $i] :
( Z2
@ ^ [Z5: $i > $i,Z6: $i] :
( esk3_0
@ ^ [Z7: $i,Z8: $i] : c_Empty
@ ^ [Z7: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty )
@ c_Empty
@ ( esk2_0
@ ^ [Z5: $i,Z6: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ c_Empty )
@ ( c_Inj0
@ ( esk4_0
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) )
@ ^ [Z0: $i] :
( esk4_0
@ ^ [Z1: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ^ [Z1: $i] :
( esk3_0
@ ^ [Z2: $i,Z3: $i] : c_Empty
@ ^ [Z2: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) ) )
@ ( c_setsum
@ ( c_setsum @ X695
@ ( esk2_0
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( c_Inj0 @ c_Empty )
@ ( esk3_0
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ ^ [Z0: $i] : c_Empty
@ c_Empty
@ c_Empty
@ c_Empty ) ) )
@ ( esk2_0
@ ^ [Z0: $i,Z1: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_Inj0
@ ( esk1_0
@ ^ [Z2: $i > $i,Z3: ( $i > $i > $i ) > $i > $i,Z4: $i,Z5: $i > $i] : c_Empty
@ ^ [Z2: $i,Z3: $i,Z4: $i > $i] : c_Empty ) )
@ X695 ) )
@ ( c_setsum
@ ( c_setsum @ X696
@ ( esk3_0
@ ^ [Z0: $i,Z1: $i] : Z1
@ ^ [Z0: $i] :
( X697
@ ^ [Z1: $i > $i > $i,Z2: $i] : c_Empty )
@ ( X694 @ c_Empty
@ ^ [Z0: $i,Z1: $i] : c_Empty
@ c_Empty )
@ ( c_Inj0 @ c_Empty )
@ ( esk4_0
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z0: $i] : c_Empty ) ) )
@ ( X694
@ ( esk4_0
@ ^ [Z0: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z0: $i] :
( esk1_0
@ ^ [Z1: $i > $i,Z2: ( $i > $i > $i ) > $i > $i,Z3: $i,Z4: $i > $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty ) )
@ ^ [Z0: $i] :
( esk2_0
@ ^ [Z1: $i,Z2: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( Z2
@ ^ [Z3: $i > $i,Z4: $i] : c_Empty
@ c_Empty
@ c_Empty ) )
@ X695 ) ) ) )
& ( ( esk1_0
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] : c_Empty
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( esk1_0
@ ^ [Z3: $i > $i,Z4: ( $i > $i > $i ) > $i > $i,Z5: $i,Z6: $i > $i] :
( esk3_0
@ ^ [Z7: $i,Z8: $i] : ( Z6 @ Z5 )
@ ^ [Z7: $i] : Z7
@ c_Empty
@ ( Z6
@ ( esk4_0
@ ^ [Z7: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z7: $i] : c_Empty ) )
@ ( esk1_0
@ ^ [Z7: $i > $i,Z8: ( $i > $i > $i ) > $i > $i,Z9: $i,Z10: $i > $i] : ( c_Inj0 @ c_Empty )
@ ^ [Z7: $i,Z8: $i,Z9: $i > $i] :
( esk2_0
@ ^ [Z10: $i,Z11: ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ c_Empty ) ) )
@ ^ [Z3: $i,Z4: $i,Z5: $i > $i] :
( c_Inj1
@ ( esk1_0
@ ^ [Z6: $i > $i,Z7: ( $i > $i > $i ) > $i > $i,Z8: $i,Z9: $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: $i,Z8: $i > $i] : ( Z5 @ c_Empty ) ) ) ) )
= ( esk1_0
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] :
( c_setsum
@ ( esk1_0
@ ^ [Z4: $i > $i,Z5: ( $i > $i > $i ) > $i > $i,Z6: $i,Z7: $i > $i] : c_Empty
@ ^ [Z4: $i,Z5: $i,Z6: $i > $i] : c_Empty )
@ c_Empty )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) )
& ( ( esk1_0
@ ^ [Z0: $i > $i,Z1: ( $i > $i > $i ) > $i > $i,Z2: $i,Z3: $i > $i] : c_Empty
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] : c_Empty )
= X698 )
& ~ c_False ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7])])])])])]) ).
thf(c_0_11,plain,
! [X582: $i,X583: $i] :
( ( c_Subq @ X582 @ X583 )
<=> ! [X9: $i] :
( ( c_In @ X9 @ X582 )
=> ( c_In @ X9 @ X583 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax17])]) ).
thf(c_0_12,plain,
! [X1470: $i] :
( ( esk45_0 @ X1470 )
= X1470 ),
inference(variable_rename,[status(thm)],]) ).
thf(c_0_13,plain,
! [X1103: $i > $i,X1102: $i,X1101: $i] :
( ( esk43_0 @ X1101 @ X1102 @ X1103 )
= c_Empty ),
introduced(definition) ).
thf(c_0_14,plain,
! [X1100: $i > $i,X1099: $i,X1098: ( $i > $i > $i ) > $i > $i,X1097: $i > $i] :
( ( esk42_0 @ X1097 @ X1098 @ X1099 @ X1100 )
= c_Empty ),
introduced(definition) ).
thf(c_0_15,axiom,
! [X10: $i,X2: $i] :
( ( ~ ( c_In @ X2 @ ( c_Power @ X10 ) )
| ( ( ~ ( c_Subq @ X2 @ X10 )
| ( c_iff @ $true @ $true ) )
& ( ( c_Subq @ X2 @ X10 )
| ( c_iff @ $true @ $false ) ) ) )
& ( ( c_In @ X2 @ ( c_Power @ X10 ) )
| ( ( ~ ( c_Subq @ X2 @ X10 )
| ( c_iff @ $false @ $true ) )
& ( ( c_Subq @ X2 @ X10 )
| ( c_iff @ $false @ $false ) ) ) ) ),
inference(fool_unroll,[status(thm)],[ax7]) ).
thf(c_0_16,plain,
! [X702: $i] :
( ( ~ ( c_In @ X702 @ c_Empty )
| ( c_not @ $true ) )
& ( ( c_In @ esk5_0 @ c_Empty )
| ( c_not @ $false ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
thf(c_0_17,plain,
( c_False
| ~ ( c_not @ $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9])])]) ).
thf(c_0_18,negated_conjecture,
~ c_False,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_19,plain,
! [X721: $i,X722: $i,X723: $i,X724: $i,X725: $i] :
( ( ~ ( c_Subq @ X721 @ X722 )
| ~ ( c_In @ X723 @ X721 )
| ( c_In @ X723 @ X722 ) )
& ( ( c_In @ ( esk13_2 @ X724 @ X725 ) @ X724 )
| ( c_Subq @ X724 @ X725 ) )
& ( ~ ( c_In @ ( esk13_2 @ X724 @ X725 ) @ X725 )
| ( c_Subq @ X724 @ X725 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])])]) ).
thf(c_0_20,plain,
! [X2: $i] :
( ( esk45_0 @ X2 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i] :
( ( esk1_0 @ esk42_0 @ esk43_0 )
= X2 ),
inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10]),c_0_13]),c_0_14]) ).
thf(c_0_22,plain,
! [X743: $i,X744: $i] :
( ( ~ ( c_Subq @ X744 @ X743 )
| ( c_iff @ $true @ $true )
| ~ ( c_In @ X744 @ ( c_Power @ X743 ) ) )
& ( ( c_Subq @ X744 @ X743 )
| ( c_iff @ $true @ $false )
| ~ ( c_In @ X744 @ ( c_Power @ X743 ) ) )
& ( ~ ( c_Subq @ X744 @ X743 )
| ( c_iff @ $false @ $true )
| ( c_In @ X744 @ ( c_Power @ X743 ) ) )
& ( ( c_Subq @ X744 @ X743 )
| ( c_iff @ $false @ $false )
| ( c_In @ X744 @ ( c_Power @ X743 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_15])])]) ).
thf(c_0_23,plain,
! [X775: $o,X776: $o] :
( ( ~ X775
| X776
| ~ ( c_iff @ X775 @ X776 ) )
& ( ~ X776
| X775
| ~ ( c_iff @ X775 @ X776 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).
thf(c_0_24,plain,
! [X2: $i] :
( ( c_not @ $true )
| ~ ( c_In @ X2 @ c_Empty ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_25,plain,
~ ( c_not @ $true ),
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_26,plain,
! [X2: $i,X6: $i] :
( ( c_In @ ( esk13_2 @ X2 @ X6 ) @ X2 )
| ( c_Subq @ X2 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_27,plain,
! [X2: $i] : ( c_Empty = X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
thf(c_0_28,plain,
! [X2: $i,X6: $i] :
( ( c_iff @ ~ $true @ $true )
| ( c_In @ X2 @ ( c_Power @ X6 ) )
| ~ ( c_Subq @ X2 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,plain,
~ ( c_iff @ ~ $true @ $true ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_23])])]) ).
thf(c_0_30,plain,
! [X2: $i] :
~ ( c_In @ X2 @ c_Empty ),
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_31,plain,
! [X2: $i,X6: $i] :
( ( c_Subq @ X2 @ X6 )
| ~ ( c_In @ ( esk13_2 @ X2 @ X6 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_32,plain,
! [X2: $i,X6: $i] :
( ( c_In @ c_Empty @ X2 )
| ( c_Subq @ X2 @ X6 ) ),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_33,plain,
! [X2: $i,X6: $i] :
~ ( c_Subq @ X2 @ X6 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_27]),c_0_29]),c_0_30]) ).
thf(c_0_34,plain,
! [X2: $i,X6: $i] :
( ( c_Subq @ X2 @ X6 )
| ~ ( c_In @ c_Empty @ X6 ) ),
inference(rw,[status(thm)],[c_0_31,c_0_27]) ).
thf(c_0_35,plain,
! [X2: $i] : ( c_In @ c_Empty @ X2 ),
inference(sr,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO856^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 10:32:08 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.76/16.77 # Version: 3.1.0-ho
% 49.76/16.77 # partial match(2): HSLMSMSSSSLCHSA
% 49.76/16.77 # Preprocessing class: HSLMSLSSSSLCHHA.
% 49.76/16.77 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.76/16.77 # Starting pre_casc_6 with 1500s (5) cores
% 49.76/16.77 # Starting ehoh_best7 with 300s (1) cores
% 49.76/16.77 # Starting new_bool_8 with 300s (1) cores
% 49.76/16.77 # Starting new_ho_11 with 300s (1) cores
% 49.76/16.77 # new_bool_8 with pid 22326 completed with status 8
% 49.76/16.77 # pre_casc_6 with pid 22324 completed with status 0
% 49.76/16.77 # Result found by pre_casc_6
% 49.76/16.77 # partial match(2): HSLMSMSSSSLCHSA
% 49.76/16.77 # Preprocessing class: HSLMSLSSSSLCHHA.
% 49.76/16.77 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.76/16.77 # Starting pre_casc_6 with 1500s (5) cores
% 49.76/16.77 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 49.76/16.77 # Search class: HGHSM-SMLM31-DHHFFSBC
% 49.76/16.77 # partial match(2): HGHSM-SMLM32-DHFFFSBC
% 49.76/16.77 # Scheduled 6 strats onto 5 cores with 1485 seconds (1485 total)
% 49.76/16.77 # Starting ho_unfolding_3 with 573s (1) cores
% 49.76/16.77 # Starting pre_casc_6 with 149s (1) cores
% 49.76/16.77 # Starting full_lambda_6 with 191s (1) cores
% 49.76/16.77 # Starting ehoh_best_sine with 191s (1) cores
% 49.76/16.77 # Starting ehoh_best8_lambda with 191s (1) cores
% 49.76/16.77 # ho_unfolding_3 with pid 22904 completed with status 0
% 49.76/16.77 # Result found by ho_unfolding_3
% 49.76/16.77 # partial match(2): HSLMSMSSSSLCHSA
% 49.76/16.77 # Preprocessing class: HSLMSLSSSSLCHHA.
% 49.76/16.77 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.76/16.77 # Starting pre_casc_6 with 1500s (5) cores
% 49.76/16.77 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 49.76/16.77 # Search class: HGHSM-SMLM31-DHHFFSBC
% 49.76/16.77 # partial match(2): HGHSM-SMLM32-DHFFFSBC
% 49.76/16.77 # Scheduled 6 strats onto 5 cores with 1485 seconds (1485 total)
% 49.76/16.77 # Starting ho_unfolding_3 with 573s (1) cores
% 49.76/16.77 # Preprocessing time : 0.050 s
% 49.76/16.77 # Presaturation interreduction done
% 49.76/16.77
% 49.76/16.77 # Proof found!
% 49.76/16.77 # SZS status Theorem
% 49.76/16.77 # SZS output start CNFRefutation
% See solution above
% 49.76/16.77 # Parsed axioms : 213
% 49.76/16.77 # Removed by relevancy pruning/SinE : 145
% 49.76/16.77 # Initial clauses : 465178
% 49.76/16.77 # Removed in clause preprocessing : 463015
% 49.76/16.77 # Initial clauses in saturation : 2163
% 49.76/16.77 # Processed clauses : 789
% 49.76/16.77 # ...of these trivial : 166
% 49.76/16.77 # ...subsumed : 387
% 49.76/16.77 # ...remaining for further processing : 236
% 49.76/16.77 # Other redundant clauses eliminated : 3
% 49.76/16.77 # Clauses deleted for lack of memory : 0
% 49.76/16.77 # Backward-subsumed : 30
% 49.76/16.77 # Backward-rewritten : 17
% 49.76/16.77 # Generated clauses : 5
% 49.76/16.77 # ...of the previous two non-redundant : 9
% 49.76/16.77 # ...aggressively subsumed : 0
% 49.76/16.77 # Contextual simplify-reflections : 23
% 49.76/16.77 # Paramodulations : 0
% 49.76/16.77 # Factorizations : 0
% 49.76/16.77 # NegExts : 0
% 49.76/16.77 # Equation resolutions : 3
% 49.76/16.77 # Disequality decompositions : 0
% 49.76/16.77 # Total rewrite steps : 496
% 49.76/16.77 # ...of those cached : 305
% 49.76/16.77 # Propositional unsat checks : 0
% 49.76/16.77 # Propositional check models : 0
% 49.76/16.77 # Propositional check unsatisfiable : 0
% 49.76/16.77 # Propositional clauses : 0
% 49.76/16.77 # Propositional clauses after purity: 0
% 49.76/16.77 # Propositional unsat core size : 0
% 49.76/16.77 # Propositional preprocessing time : 0.000
% 49.76/16.77 # Propositional encoding time : 0.000
% 49.76/16.77 # Propositional solver time : 0.000
% 49.76/16.77 # Success case prop preproc time : 0.000
% 49.76/16.77 # Success case prop encoding time : 0.000
% 49.76/16.77 # Success case prop solver time : 0.000
% 49.76/16.77 # Current number of processed clauses : 184
% 49.76/16.77 # Positive orientable unit clauses : 18
% 49.76/16.77 # Positive unorientable unit clauses: 3
% 49.76/16.77 # Negative unit clauses : 17
% 49.76/16.77 # Non-unit-clauses : 146
% 49.76/16.77 # Current number of unprocessed clauses: 1383
% 49.76/16.77 # ...number of literals in the above : 7693
% 49.76/16.77 # Current number of archived formulas : 0
% 49.76/16.77 # Current number of archived clauses : 49
% 49.76/16.77 # Clause-clause subsumption calls (NU) : 10140
% 49.76/16.77 # Rec. Clause-clause subsumption calls : 7276
% 49.76/16.77 # Non-unit clause-clause subsumptions : 53
% 49.76/16.77 # Unit Clause-clause subsumption calls : 923
% 49.76/16.77 # Rewrite failures with RHS unbound : 0
% 49.76/16.77 # BW rewrite match attempts : 52
% 49.76/16.77 # BW rewrite match successes : 18
% 49.76/16.77 # Condensation attempts : 789
% 49.76/16.77 # Condensation successes : 0
% 49.76/16.77 # Termbank termtop insertions : 19584794
% 49.76/16.77 # Search garbage collected termcells : 1981991
% 49.76/16.77
% 49.76/16.77 # -------------------------------------------------
% 49.76/16.77 # User time : 14.806 s
% 49.76/16.77 # System time : 0.979 s
% 49.76/16.77 # Total time : 15.785 s
% 49.76/16.77 # Maximum resident set size: 1250004 pages
% 49.76/16.77
% 49.76/16.77 # -------------------------------------------------
% 49.76/16.77 # User time : 15.767 s
% 49.76/16.77 # System time : 1.439 s
% 49.76/16.77 # Total time : 17.206 s
% 49.76/16.77 # Maximum resident set size: 2368 pages
% 49.76/16.77 % E---3.1 exiting
% 49.76/16.78 % E exiting
%------------------------------------------------------------------------------