TSTP Solution File: SYO854^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO854^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 08:50:14 EDT 2024
% Result : Theorem 54.70s 18.23s
% Output : CNFRefutation 54.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 58 ( 15 unt; 21 typ; 0 def)
% Number of atoms : 144 ( 32 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1253 ( 35 ~; 38 |; 22 &;1133 @)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1803 (1803 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 6 con; 0-5 aty)
% Number of variables : 973 ( 828 ^ 142 !; 3 ?; 973 :)
% 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_268,type,
esk1_0: $i ).
thf(decl_280,type,
epred143_0: $o ).
thf(decl_283,type,
esk13_2: $i > $i > $i ).
thf(decl_326,type,
esk52_0: ( $i > $i ) > ( $i > $i > ( $i > $i ) > $i ) > $i ).
thf(decl_327,type,
esk53_0: ( ( $i > ( ( $i > $i ) > $i > $i ) > $i > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > ( ( $i > ( $i > $i ) > $i ) > $i ) > $i ).
thf(decl_328,type,
esk54_0: ( ( $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > ( $i > $i ) > $i ) > $i > $i ).
thf(decl_329,type,
esk55_0: ( ( ( ( $i > $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i ) > $i > $i ).
thf(decl_503,type,
esk221_1: $i > $i > $i ).
thf(decl_549,type,
esk262_0: ( $i > ( ( $i > $i ) > $i > $i ) > $i > $i ) > $i > $i > ( $i > $i ) > $i > $i ).
thf(decl_550,type,
esk263_0: ( $i > ( $i > $i ) > $i ) > $i > $i > $i > $i ).
thf(decl_551,type,
esk264_1: ( ( $i > $i > $i > $i ) > $i ) > ( $i > ( $i > $i ) > $i ) > $i ).
thf(ax13,axiom,
( c_not
= ( ^ [X17: $o] :
( X17
=> c_False ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(ax5,axiom,
( c_not
@ ? [X7: $i] : ( c_In @ X7 @ c_Empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(ax11,axiom,
( c_False
<=> ! [X15: $o] : X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(conj,conjecture,
! [X201: ( $i > $i ) > ( $i > $i > ( $i > $i ) > $i ) > $i,X202: ( ( $i > ( ( $i > $i ) > $i > $i ) > $i > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > ( ( $i > ( $i > $i ) > $i ) > $i ) > $i,X203: ( ( $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > ( $i > $i ) > $i ) > $i > $i,X204: ( ( ( ( $i > $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i ) > $i > $i] :
( ! [X66: $i,X205: $i,X83: $i,X206: ( $i > $i ) > $i] :
( ( X204
@ ^ [X207: ( ( $i > $i > $i ) > $i > $i ) > $i,X208: $i > $i > $i] :
( X203
@ ^ [X209: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X210: $i,X211: ( $i > $i ) > $i,X212: $i > $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( X208 @ ( c_Inj1 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) )
@ ( X201
@ ^ [X213: $i] : X213
@ ^ [X214: $i,X215: $i,X216: $i > $i] :
( c_setsum
@ ( X202
@ ^ [X217: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X172: $i,X173: $i,X218: $i > $i,X181: $i] : c_Empty
@ ^ [X219: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( X203
@ ^ [X220: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( X204
@ ^ [X221: ( ( $i > $i > $i ) > $i > $i ) > $i,X168: $i > $i > $i] : c_Empty
@ X205 )
@ ( X203
@ ^ [X222: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X206
@ ^ [X223: $i] : c_Empty )
@ ^ [X224: $i,X225: ( $i > $i ) > $i,X226: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( X201
@ ^ [X227: $i] : c_Empty
@ ^ [X228: $i,X229: $i,X230: $i > $i] : c_Empty ) ) )
@ ^ [X231: $i,X232: ( $i > $i ) > $i,X233: $i > $i] : X231
@ X66 ) )
= ( c_setsum @ X205 @ X66 ) )
=> ( ! [X234: ( $i > ( $i > $i ) > $i ) > $i,X235: $i,X83: $i,X236: $i] :
( ( X204
@ ^ [X237: ( ( $i > $i > $i ) > $i > $i ) > $i,X238: $i > $i > $i] : c_Empty
@ c_Empty )
= ( c_setsum @ c_Empty
@ ( X234
@ ^ [X239: $i,X240: $i > $i] : c_Empty ) ) )
=> ( ! [X241: $i > ( $i > $i ) > ( $i > $i ) > $i > $i,X242: $i > $i > ( $i > $i ) > $i,X83: $i,X243: $i > $i] :
( ( X203
@ ^ [X244: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X201
@ ^ [X245: $i] : c_Empty
@ ^ [X246: $i,X247: $i,X248: $i > $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [X249: $i,X250: ( $i > $i ) > $i,X251: $i > $i] :
( c_setsum
@ ( X201
@ ^ [X252: $i] :
( c_setsum @ X252
@ ( X202
@ ^ [X253: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X254: $i,X172: $i,X255: $i > $i,X174: $i] : c_Empty
@ ^ [X256: $i > ( $i > $i ) > $i] : c_Empty ) )
@ ^ [X257: $i,X258: $i,X259: $i > $i] : ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_setsum @ c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( X204
@ ^ [X260: ( ( $i > $i > $i ) > $i > $i ) > $i,X170: $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ( X241
@ ( X204
@ ^ [X261: ( ( $i > $i > $i ) > $i > $i ) > $i,X262: $i > $i > $i] : c_Empty
@ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
@ ^ [X263: $i] : ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) )
@ ^ [X264: $i] :
( c_setsum @ c_Empty
@ ( c_setsum @ c_Empty
@ ( X242 @ c_Empty @ c_Empty
@ ^ [X265: $i] : c_Empty ) ) )
@ ( X202
@ ^ [X266: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X267: $i,X268: $i,X269: $i > $i,X270: $i] : c_Empty
@ ^ [X271: $i > ( $i > $i ) > $i] : c_Empty ) ) )
= ( X201
@ ^ [X272: $i] :
( X201
@ ^ [X273: $i] : c_Empty
@ ^ [X274: $i,X275: $i,X276: $i > $i] :
( c_setsum
@ ( X202
@ ^ [X277: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X278: $i,X172: $i,X279: $i > $i,X174: $i] : c_Empty
@ ^ [X280: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_Inj1 @ X275 ) ) )
@ ^ [X281: $i,X282: $i,X283: $i > $i] :
( c_setsum
@ ( X243
@ ( c_setsum @ X282
@ ( X202
@ ^ [X284: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X285: $i,X286: $i,X287: $i > $i,X173: $i] : c_Empty
@ ^ [X288: $i > ( $i > $i ) > $i] : c_Empty ) ) )
@ c_Empty ) ) )
=> ( ! [X289: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i,X290: $i,X83: $i,X291: $i] :
( ( X203
@ ^ [X292: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum @ c_Empty
@ ( c_setsum
@ ( c_setsum
@ ( X203
@ ^ [X293: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X294: $i,X295: ( $i > $i ) > $i,X296: $i > $i] : c_Empty
@ c_Empty )
@ ( X204
@ ^ [X297: ( ( $i > $i > $i ) > $i > $i ) > $i,X168: $i > $i > $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) )
@ ^ [X298: $i,X299: ( $i > $i ) > $i,X300: $i > $i] :
( c_setsum @ ( c_setsum @ c_Empty @ X291 )
@ ( X202
@ ^ [X301: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X302: $i,X303: $i,X304: $i > $i,X173: $i] :
( X204
@ ^ [X305: ( ( $i > $i > $i ) > $i > $i ) > $i,X306: $i > $i > $i] : ( X304 @ c_Empty )
@ X302 )
@ ^ [X307: $i > ( $i > $i ) > $i] :
( c_Inj1
@ ( X202
@ ^ [X308: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X309: $i,X172: $i,X310: $i > $i,X174: $i] : c_Empty
@ ^ [X311: $i > ( $i > $i ) > $i] : c_Empty ) ) ) )
@ c_Empty )
= ( X289
@ ^ [X312: $i,X313: $i > $i,X314: $i] :
( X204
@ ^ [X315: ( ( $i > $i > $i ) > $i > $i ) > $i,X170: $i > $i > $i] :
( X170
@ ( X202
@ ^ [X316: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X172: $i,X173: $i,X317: $i > $i,X181: $i] :
( X203
@ ^ [X318: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X188: $i,X319: ( $i > $i ) > $i,X320: $i > $i] : c_Empty
@ c_Empty )
@ ^ [X321: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_Inj0 @ c_Empty ) )
@ ( X313 @ c_Empty ) )
@ ^ [X322: $i > $i] : c_Empty ) )
=> ( ! [X323: ( $i > $i > $i > $i ) > $i,X324: $i,X83: $i,X325: ( $i > $i > $i > $i ) > $i] :
( ( X202
@ ^ [X326: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X327: $i,X328: $i,X329: $i > $i,X330: $i] : X327
@ ^ [X331: $i > ( $i > $i ) > $i] :
( c_setsum @ c_Empty
@ ( c_setsum
@ ( X325
@ ^ [X332: $i,X333: $i,X334: $i] :
( X331 @ c_Empty
@ ^ [X335: $i] : c_Empty ) )
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( X331 @ c_Empty
@ ^ [X336: $i] : c_Empty ) ) ) ) )
= X324 )
=> ( ! [X337: ( ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i > $i > $i,X338: ( ( $i > $i ) > $i ) > $i,X339: $i > $i,X340: $i > ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i] :
( ( X202
@ ^ [X341: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X342: $i,X343: $i,X344: $i > $i,X345: $i] :
( c_setsum
@ ( X203
@ ^ [X346: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X203
@ ^ [X347: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X172: $i,X348: ( $i > $i ) > $i,X349: $i > $i] : c_Empty
@ c_Empty ) )
@ ^ [X350: $i,X351: ( $i > $i ) > $i,X352: $i > $i] :
( X203
@ ^ [X353: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X351
@ ^ [X181: $i] : c_Empty )
@ ^ [X174: $i,X354: ( $i > $i ) > $i,X355: $i > $i] :
( X203
@ ^ [X356: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X357: $i,X358: ( $i > $i ) > $i,X359: $i > $i] : c_Empty
@ c_Empty )
@ ( X351
@ ^ [X174: $i] : c_Empty ) )
@ ( c_Inj0 @ ( X344 @ c_Empty ) ) )
@ X342 )
@ ^ [X360: $i > ( $i > $i ) > $i] :
( X360 @ c_Empty
@ ^ [X361: $i] : c_Empty ) )
= ( X337
@ ^ [X362: ( $i > $i ) > $i > $i,X363: $i,X364: $i] :
( X202
@ ^ [X365: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X366: $i,X367: $i,X368: $i > $i,X173: $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X204
@ ^ [X369: ( ( $i > $i > $i ) > $i > $i ) > $i,X370: $i > $i > $i] :
( X203
@ ^ [X371: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X188: $i,X319: ( $i > $i ) > $i,X320: $i > $i] : c_Empty
@ c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
@ ^ [X372: $i > ( $i > $i ) > $i] :
( X204
@ ^ [X373: ( ( $i > $i > $i ) > $i > $i ) > $i,X171: $i > $i > $i] :
( c_setsum
@ ( X373
@ ^ [X374: $i > $i > $i,X173: $i] : c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) )
@ ( X204
@ ^ [X375: ( ( $i > $i > $i ) > $i > $i ) > $i,X376: $i > $i > $i] :
( X201
@ ^ [X377: $i] :
( X375
@ ^ [X169: $i > $i > $i,X378: $i] :
( X202
@ ^ [X379: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X172: $i,X173: $i,X380: $i > $i,X181: $i] : c_Empty
@ ^ [X381: $i > ( $i > $i ) > $i] : c_Empty ) )
@ ^ [X382: $i,X383: $i,X384: $i > $i] :
( X201
@ ^ [X385: $i] :
( X201
@ ^ [X172: $i] : c_Empty
@ ^ [X172: $i,X173: $i,X386: $i > $i] : c_Empty )
@ ^ [X387: $i,X172: $i,X388: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X339
@ ( X340 @ c_Empty
@ ^ [X389: $i > $i] : c_Empty
@ ^ [X390: $i] : c_Empty
@ c_Empty ) ) ) )
@ ( X338
@ ^ [X391: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
=> ( ! [X66: $i,X82: $i > $i,X392: $i > ( ( $i > $i ) > $i ) > $i,X393: ( $i > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i] :
( ( X201
@ ^ [X394: $i] :
( X204
@ ^ [X395: ( ( $i > $i > $i ) > $i > $i ) > $i,X168: $i > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty
@ ( c_Inj0
@ ( X203
@ ^ [X396: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X397: $i,X398: ( $i > $i ) > $i,X399: $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ^ [X400: $i,X401: $i,X402: $i > $i] :
( X203
@ ^ [X403: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X404: $i,X405: ( $i > $i ) > $i,X406: $i > $i] :
( c_setsum
@ ( X203
@ ^ [X407: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X172: $i,X408: ( $i > $i ) > $i,X409: $i > $i] : c_Empty
@ ( X405
@ ^ [X172: $i] : c_Empty ) )
@ ( c_Inj1
@ ( X202
@ ^ [X410: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X173: $i,X174: $i,X411: $i > $i,X188: $i] : c_Empty
@ ^ [X412: $i > ( $i > $i ) > $i] : c_Empty ) ) )
@ c_Empty ) )
= ( X203
@ ^ [X413: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( X413 @ c_Empty
@ ^ [X414: $i > $i,X415: $i] : ( c_Inj1 @ ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ c_Empty
@ ( X204
@ ^ [X416: ( ( $i > $i > $i ) > $i > $i ) > $i,X168: $i > $i > $i] : c_Empty
@ c_Empty ) )
@ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
@ ( X202
@ ^ [X417: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,X418: $i,X419: $i,X420: $i > $i,X421: $i] : ( c_Inj0 @ c_Empty )
@ ^ [X422: $i > ( $i > $i ) > $i] :
( c_Inj1
@ ( X204
@ ^ [X423: ( ( $i > $i > $i ) > $i > $i ) > $i,X169: $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ^ [X424: $i,X425: ( $i > $i ) > $i,X426: $i > $i] :
( c_setsum
@ ( X203
@ ^ [X427: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X428: $i,X429: ( $i > $i ) > $i,X430: $i > $i] :
( c_Inj1
@ ( X203
@ ^ [X431: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X172: $i,X432: ( $i > $i ) > $i,X433: $i > $i] : c_Empty
@ c_Empty ) )
@ ( X393
@ ^ [X434: $i,X435: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( X203
@ ^ [X436: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [X437: $i,X438: ( $i > $i ) > $i,X439: $i > $i] : c_Empty
@ c_Empty )
@ ^ [X440: $i] : X424 ) )
@ ( X425
@ ^ [X441: $i] :
( c_Inj1
@ ( X201
@ ^ [X442: $i] : c_Empty
@ ^ [X443: $i,X444: $i,X445: $i > $i] : c_Empty ) ) ) )
@ ( X203
@ ^ [X446: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( X82 @ ( X82 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ^ [X447: $i,X448: ( $i > $i ) > $i,X449: $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
=> ( ! [X66: $i,X450: $i,X83: $i,X451: $i] :
( ( X201
@ ^ [X452: $i] : X452
@ ^ [X453: $i,X454: $i,X455: $i > $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) )
= ( c_Inj0 @ c_Empty ) )
=> c_False ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
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(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(c_0_7,plain,
! [X521: $o] :
( ( c_not @ X521 )
<=> ( X521
=> c_False ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax13])]) ).
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,
! [X769: $o] :
( ( ~ ( c_not @ X769 )
| ~ X769
| c_False )
& ( X769
| ( c_not @ X769 ) )
& ( ~ c_False
| ( c_not @ X769 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
thf(c_0_10,plain,
! [X767: $o] :
( ( ~ c_False
| X767 )
& ( ~ epred143_0
| 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)],[ax11])])])])]) ).
thf(c_0_11,negated_conjecture,
~ ! [X201: ( $i > $i ) > ( $i > $i > ( $i > $i ) > $i ) > $i,X202: ( ( $i > ( ( $i > $i ) > $i > $i ) > $i > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > ( ( $i > ( $i > $i ) > $i ) > $i ) > $i,X203: ( ( $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i ) > ( $i > ( ( $i > $i ) > $i ) > ( $i > $i ) > $i ) > $i > $i,X204: ( ( ( ( $i > $i > $i ) > $i > $i ) > $i ) > ( $i > $i > $i ) > $i ) > $i > $i] :
( ! [X66: $i,X205: $i,X83: $i,X206: ( $i > $i ) > $i] :
( ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > $i > $i ) > $i,Z1: $i > $i > $i] :
( X203
@ ^ [Z2: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z2: $i,Z3: ( $i > $i ) > $i,Z4: $i > $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( Z1 @ ( c_Inj1 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) )
@ ( X201
@ ^ [Z2: $i] : Z2
@ ^ [Z2: $i,Z3: $i,Z4: $i > $i] :
( c_setsum
@ ( X202
@ ^ [Z5: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z6: $i,Z7: $i,Z8: $i > $i,Z9: $i] : c_Empty
@ ^ [Z5: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( X203
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( X204
@ ^ [Z1: ( ( $i > $i > $i ) > $i > $i ) > $i,Z2: $i > $i > $i] : c_Empty
@ X205 )
@ ( X203
@ ^ [Z1: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X206
@ ^ [Z2: $i] : c_Empty )
@ ^ [Z1: $i,Z2: ( $i > $i ) > $i,Z3: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( X201
@ ^ [Z1: $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty ) ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] : Z0
@ X66 ) )
= ( c_setsum @ X205 @ X66 ) )
=> ( ! [X234: ( $i > ( $i > $i ) > $i ) > $i,X235: $i,X83: $i,X236: $i] :
( ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > $i > $i ) > $i,Z1: $i > $i > $i] : c_Empty
@ c_Empty )
= ( c_setsum @ c_Empty
@ ( X234
@ ^ [Z0: $i,Z1: $i > $i] : c_Empty ) ) )
=> ( ! [X241: $i > ( $i > $i ) > ( $i > $i ) > $i > $i,X242: $i > $i > ( $i > $i ) > $i,X83: $i,X243: $i > $i] :
( ( X203
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X201
@ ^ [Z1: $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] :
( c_setsum
@ ( X201
@ ^ [Z3: $i] :
( c_setsum @ Z3
@ ( X202
@ ^ [Z4: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z5: $i,Z6: $i,Z7: $i > $i,Z8: $i] : c_Empty
@ ^ [Z4: $i > ( $i > $i ) > $i] : c_Empty ) )
@ ^ [Z3: $i,Z4: $i,Z5: $i > $i] : ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_setsum @ c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( X204
@ ^ [Z3: ( ( $i > $i > $i ) > $i > $i ) > $i,Z4: $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ( X241
@ ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > $i > $i ) > $i,Z1: $i > $i > $i] : c_Empty
@ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
@ ^ [Z0: $i] : ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) )
@ ^ [Z0: $i] :
( c_setsum @ c_Empty
@ ( c_setsum @ c_Empty
@ ( X242 @ c_Empty @ c_Empty
@ ^ [Z1: $i] : c_Empty ) ) )
@ ( X202
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z1: $i,Z2: $i,Z3: $i > $i,Z4: $i] : c_Empty
@ ^ [Z0: $i > ( $i > $i ) > $i] : c_Empty ) ) )
= ( X201
@ ^ [Z0: $i] :
( X201
@ ^ [Z1: $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] :
( c_setsum
@ ( X202
@ ^ [Z4: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z5: $i,Z6: $i,Z7: $i > $i,Z8: $i] : c_Empty
@ ^ [Z4: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_Inj1 @ Z2 ) ) )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( c_setsum
@ ( X243
@ ( c_setsum @ Z1
@ ( X202
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z4: $i,Z5: $i,Z6: $i > $i,Z7: $i] : c_Empty
@ ^ [Z3: $i > ( $i > $i ) > $i] : c_Empty ) ) )
@ c_Empty ) ) )
=> ( ! [X289: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i,X290: $i,X83: $i,X291: $i] :
( ( X203
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum @ c_Empty
@ ( c_setsum
@ ( c_setsum
@ ( X203
@ ^ [Z1: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z1: $i,Z2: ( $i > $i ) > $i,Z3: $i > $i] : c_Empty
@ c_Empty )
@ ( X204
@ ^ [Z1: ( ( $i > $i > $i ) > $i > $i ) > $i,Z2: $i > $i > $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] :
( c_setsum @ ( c_setsum @ c_Empty @ X291 )
@ ( X202
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z4: $i,Z5: $i,Z6: $i > $i,Z7: $i] :
( X204
@ ^ [Z8: ( ( $i > $i > $i ) > $i > $i ) > $i,Z9: $i > $i > $i] : ( Z6 @ c_Empty )
@ Z4 )
@ ^ [Z3: $i > ( $i > $i ) > $i] :
( c_Inj1
@ ( X202
@ ^ [Z4: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z5: $i,Z6: $i,Z7: $i > $i,Z8: $i] : c_Empty
@ ^ [Z4: $i > ( $i > $i ) > $i] : c_Empty ) ) ) )
@ c_Empty )
= ( X289
@ ^ [Z0: $i,Z1: $i > $i,Z2: $i] :
( X204
@ ^ [Z3: ( ( $i > $i > $i ) > $i > $i ) > $i,Z4: $i > $i > $i] :
( Z4
@ ( X202
@ ^ [Z5: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z6: $i,Z7: $i,Z8: $i > $i,Z9: $i] :
( X203
@ ^ [Z10: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z10: $i,Z11: ( $i > $i ) > $i,Z12: $i > $i] : c_Empty
@ c_Empty )
@ ^ [Z5: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_Inj0 @ c_Empty ) )
@ ( Z1 @ c_Empty ) )
@ ^ [Z0: $i > $i] : c_Empty ) )
=> ( ! [X323: ( $i > $i > $i > $i ) > $i,X324: $i,X83: $i,X325: ( $i > $i > $i > $i ) > $i] :
( ( X202
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z1: $i,Z2: $i,Z3: $i > $i,Z4: $i] : Z1
@ ^ [Z0: $i > ( $i > $i ) > $i] :
( c_setsum @ c_Empty
@ ( c_setsum
@ ( X325
@ ^ [Z1: $i,Z2: $i,Z3: $i] :
( Z0 @ c_Empty
@ ^ [Z4: $i] : c_Empty ) )
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( Z0 @ c_Empty
@ ^ [Z1: $i] : c_Empty ) ) ) ) )
= X324 )
=> ( ! [X337: ( ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i > $i > $i,X338: ( ( $i > $i ) > $i ) > $i,X339: $i > $i,X340: $i > ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i] :
( ( X202
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z1: $i,Z2: $i,Z3: $i > $i,Z4: $i] :
( c_setsum
@ ( X203
@ ^ [Z5: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X203
@ ^ [Z6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: ( $i > $i ) > $i,Z8: $i > $i] : c_Empty
@ c_Empty ) )
@ ^ [Z5: $i,Z6: ( $i > $i ) > $i,Z7: $i > $i] :
( X203
@ ^ [Z8: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( Z6
@ ^ [Z9: $i] : c_Empty )
@ ^ [Z8: $i,Z9: ( $i > $i ) > $i,Z10: $i > $i] :
( X203
@ ^ [Z11: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z11: $i,Z12: ( $i > $i ) > $i,Z13: $i > $i] : c_Empty
@ c_Empty )
@ ( Z6
@ ^ [Z8: $i] : c_Empty ) )
@ ( c_Inj0 @ ( Z3 @ c_Empty ) ) )
@ Z1 )
@ ^ [Z0: $i > ( $i > $i ) > $i] :
( Z0 @ c_Empty
@ ^ [Z1: $i] : c_Empty ) )
= ( X337
@ ^ [Z0: ( $i > $i ) > $i > $i,Z1: $i,Z2: $i] :
( X202
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z4: $i,Z5: $i,Z6: $i > $i,Z7: $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X204
@ ^ [Z8: ( ( $i > $i > $i ) > $i > $i ) > $i,Z9: $i > $i > $i] :
( X203
@ ^ [Z10: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z10: $i,Z11: ( $i > $i ) > $i,Z12: $i > $i] : c_Empty
@ c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Z3: $i > ( $i > $i ) > $i] :
( X204
@ ^ [Z4: ( ( $i > $i > $i ) > $i > $i ) > $i,Z5: $i > $i > $i] :
( c_setsum
@ ( Z4
@ ^ [Z6: $i > $i > $i,Z7: $i] : c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) )
@ ( X204
@ ^ [Z0: ( ( $i > $i > $i ) > $i > $i ) > $i,Z1: $i > $i > $i] :
( X201
@ ^ [Z2: $i] :
( Z0
@ ^ [Z3: $i > $i > $i,Z4: $i] :
( X202
@ ^ [Z5: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z6: $i,Z7: $i,Z8: $i > $i,Z9: $i] : c_Empty
@ ^ [Z5: $i > ( $i > $i ) > $i] : c_Empty ) )
@ ^ [Z2: $i,Z3: $i,Z4: $i > $i] :
( X201
@ ^ [Z5: $i] :
( X201
@ ^ [Z6: $i] : c_Empty
@ ^ [Z6: $i,Z7: $i,Z8: $i > $i] : c_Empty )
@ ^ [Z5: $i,Z6: $i,Z7: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X339
@ ( X340 @ c_Empty
@ ^ [Z0: $i > $i] : c_Empty
@ ^ [Z0: $i] : c_Empty
@ c_Empty ) ) ) )
@ ( X338
@ ^ [Z0: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
=> ( ! [X66: $i,X82: $i > $i,X392: $i > ( ( $i > $i ) > $i ) > $i,X393: ( $i > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i] :
( ( X201
@ ^ [Z0: $i] :
( X204
@ ^ [Z1: ( ( $i > $i > $i ) > $i > $i ) > $i,Z2: $i > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty
@ ( c_Inj0
@ ( X203
@ ^ [Z1: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z1: $i,Z2: ( $i > $i ) > $i,Z3: $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( X203
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z3: $i,Z4: ( $i > $i ) > $i,Z5: $i > $i] :
( c_setsum
@ ( X203
@ ^ [Z6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: ( $i > $i ) > $i,Z8: $i > $i] : c_Empty
@ ( Z4
@ ^ [Z6: $i] : c_Empty ) )
@ ( c_Inj1
@ ( X202
@ ^ [Z6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z7: $i,Z8: $i,Z9: $i > $i,Z10: $i] : c_Empty
@ ^ [Z6: $i > ( $i > $i ) > $i] : c_Empty ) ) )
@ c_Empty ) )
= ( X203
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( Z0 @ c_Empty
@ ^ [Z1: $i > $i,Z2: $i] : ( c_Inj1 @ ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ c_Empty
@ ( X204
@ ^ [Z1: ( ( $i > $i > $i ) > $i > $i ) > $i,Z2: $i > $i > $i] : c_Empty
@ c_Empty ) )
@ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
@ ( X202
@ ^ [Z1: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z2: $i,Z3: $i,Z4: $i > $i,Z5: $i] : ( c_Inj0 @ c_Empty )
@ ^ [Z1: $i > ( $i > $i ) > $i] :
( c_Inj1
@ ( X204
@ ^ [Z2: ( ( $i > $i > $i ) > $i > $i ) > $i,Z3: $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] :
( c_setsum
@ ( X203
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z3: $i,Z4: ( $i > $i ) > $i,Z5: $i > $i] :
( c_Inj1
@ ( X203
@ ^ [Z6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: ( $i > $i ) > $i,Z8: $i > $i] : c_Empty
@ c_Empty ) )
@ ( X393
@ ^ [Z3: $i,Z4: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( X203
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z3: $i,Z4: ( $i > $i ) > $i,Z5: $i > $i] : c_Empty
@ c_Empty )
@ ^ [Z3: $i] : Z0 ) )
@ ( Z1
@ ^ [Z3: $i] :
( c_Inj1
@ ( X201
@ ^ [Z4: $i] : c_Empty
@ ^ [Z4: $i,Z5: $i,Z6: $i > $i] : c_Empty ) ) ) )
@ ( X203
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( X82 @ ( X82 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
=> ( ! [X66: $i,X450: $i,X83: $i,X451: $i] :
( ( X201
@ ^ [Z0: $i] : Z0
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) )
= ( c_Inj0 @ c_Empty ) )
=> c_False ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]) ).
thf(c_0_12,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_13,plain,
! [X736: $i] :
( ( ~ ( c_In @ X736 @ c_Empty )
| ( c_not @ $true ) )
& ( ( c_In @ esk1_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_14,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_15,plain,
~ c_False,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10])])]) ).
thf(c_0_16,negated_conjecture,
! [X1104: $i,X1105: $i,X1106: ( $i > $i ) > $i,X1107: ( $i > ( $i > $i ) > $i ) > $i,X1108: $i > ( $i > $i ) > ( $i > $i ) > $i > $i,X1109: $i > $i > ( $i > $i ) > $i,X1110: $i > $i,X1111: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i,X1112: $i,X1113: $i,X1114: ( $i > $i > $i > $i ) > $i,X1115: ( ( ( $i > $i ) > $i > $i ) > $i > $i > $i ) > $i > $i > $i,X1116: ( ( $i > $i ) > $i ) > $i,X1117: $i > $i,X1118: $i > ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i,X1119: $i > $i,X1120: ( $i > ( $i > $i ) > $i ) > $i > ( $i > $i ) > $i] :
( ( ( esk55_0
@ ^ [Z0: ( ( $i > $i > $i ) > $i > $i ) > $i,Z1: $i > $i > $i] :
( esk54_0
@ ^ [Z2: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z2: $i,Z3: ( $i > $i ) > $i,Z4: $i > $i] : ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( Z1 @ ( c_Inj1 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) )
@ ( esk52_0
@ ^ [Z2: $i] : Z2
@ ^ [Z2: $i,Z3: $i,Z4: $i > $i] :
( c_setsum
@ ( esk53_0
@ ^ [Z5: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z6: $i,Z7: $i,Z8: $i > $i,Z9: $i] : c_Empty
@ ^ [Z5: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ( esk54_0
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( esk55_0
@ ^ [Z1: ( ( $i > $i > $i ) > $i > $i ) > $i,Z2: $i > $i > $i] : c_Empty
@ X1105 )
@ ( esk54_0
@ ^ [Z1: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( X1106
@ ^ [Z2: $i] : c_Empty )
@ ^ [Z1: $i,Z2: ( $i > $i ) > $i,Z3: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( esk52_0
@ ^ [Z1: $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : c_Empty ) ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] : Z0
@ X1104 ) )
= ( c_setsum @ X1105 @ X1104 ) )
& ( ( esk55_0
@ ^ [Z0: ( ( $i > $i > $i ) > $i > $i ) > $i,Z1: $i > $i > $i] : c_Empty
@ c_Empty )
= ( c_setsum @ c_Empty
@ ( X1107
@ ^ [Z0: $i,Z1: $i > $i] : c_Empty ) ) )
& ( ( esk54_0
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( esk52_0
@ ^ [Z1: $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] :
( c_setsum
@ ( esk52_0
@ ^ [Z3: $i] :
( c_setsum @ Z3
@ ( esk53_0
@ ^ [Z4: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z5: $i,Z6: $i,Z7: $i > $i,Z8: $i] : c_Empty
@ ^ [Z4: $i > ( $i > $i ) > $i] : c_Empty ) )
@ ^ [Z3: $i,Z4: $i,Z5: $i > $i] : ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) )
@ ( c_setsum @ c_Empty
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( esk55_0
@ ^ [Z3: ( ( $i > $i > $i ) > $i > $i ) > $i,Z4: $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ( X1108
@ ( esk55_0
@ ^ [Z0: ( ( $i > $i > $i ) > $i > $i ) > $i,Z1: $i > $i > $i] : c_Empty
@ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
@ ^ [Z0: $i] : ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) )
@ ^ [Z0: $i] :
( c_setsum @ c_Empty
@ ( c_setsum @ c_Empty
@ ( X1109 @ c_Empty @ c_Empty
@ ^ [Z1: $i] : c_Empty ) ) )
@ ( esk53_0
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z1: $i,Z2: $i,Z3: $i > $i,Z4: $i] : c_Empty
@ ^ [Z0: $i > ( $i > $i ) > $i] : c_Empty ) ) )
= ( esk52_0
@ ^ [Z0: $i] :
( esk52_0
@ ^ [Z1: $i] : c_Empty
@ ^ [Z1: $i,Z2: $i,Z3: $i > $i] :
( c_setsum
@ ( esk53_0
@ ^ [Z4: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z5: $i,Z6: $i,Z7: $i > $i,Z8: $i] : c_Empty
@ ^ [Z4: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_Inj1 @ Z2 ) ) )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( c_setsum
@ ( X1110
@ ( c_setsum @ Z1
@ ( esk53_0
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z4: $i,Z5: $i,Z6: $i > $i,Z7: $i] : c_Empty
@ ^ [Z3: $i > ( $i > $i ) > $i] : c_Empty ) ) )
@ c_Empty ) ) )
& ( ( esk54_0
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum @ c_Empty
@ ( c_setsum
@ ( c_setsum
@ ( esk54_0
@ ^ [Z1: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z1: $i,Z2: ( $i > $i ) > $i,Z3: $i > $i] : c_Empty
@ c_Empty )
@ ( esk55_0
@ ^ [Z1: ( ( $i > $i > $i ) > $i > $i ) > $i,Z2: $i > $i > $i] : c_Empty
@ c_Empty ) )
@ c_Empty ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] :
( c_setsum @ ( c_setsum @ c_Empty @ X1112 )
@ ( esk53_0
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z4: $i,Z5: $i,Z6: $i > $i,Z7: $i] :
( esk55_0
@ ^ [Z8: ( ( $i > $i > $i ) > $i > $i ) > $i,Z9: $i > $i > $i] : ( Z6 @ c_Empty )
@ Z4 )
@ ^ [Z3: $i > ( $i > $i ) > $i] :
( c_Inj1
@ ( esk53_0
@ ^ [Z4: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z5: $i,Z6: $i,Z7: $i > $i,Z8: $i] : c_Empty
@ ^ [Z4: $i > ( $i > $i ) > $i] : c_Empty ) ) ) )
@ c_Empty )
= ( X1111
@ ^ [Z0: $i,Z1: $i > $i,Z2: $i] :
( esk55_0
@ ^ [Z3: ( ( $i > $i > $i ) > $i > $i ) > $i,Z4: $i > $i > $i] :
( Z4
@ ( esk53_0
@ ^ [Z5: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z6: $i,Z7: $i,Z8: $i > $i,Z9: $i] :
( esk54_0
@ ^ [Z10: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z10: $i,Z11: ( $i > $i ) > $i,Z12: $i > $i] : c_Empty
@ c_Empty )
@ ^ [Z5: $i > ( $i > $i ) > $i] : c_Empty )
@ ( c_Inj0 @ c_Empty ) )
@ ( Z1 @ c_Empty ) )
@ ^ [Z0: $i > $i] : c_Empty ) )
& ( ( esk53_0
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z1: $i,Z2: $i,Z3: $i > $i,Z4: $i] : Z1
@ ^ [Z0: $i > ( $i > $i ) > $i] :
( c_setsum @ c_Empty
@ ( c_setsum
@ ( X1114
@ ^ [Z1: $i,Z2: $i,Z3: $i] :
( Z0 @ c_Empty
@ ^ [Z4: $i] : c_Empty ) )
@ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty )
@ ( Z0 @ c_Empty
@ ^ [Z1: $i] : c_Empty ) ) ) ) )
= X1113 )
& ( ( esk53_0
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z1: $i,Z2: $i,Z3: $i > $i,Z4: $i] :
( c_setsum
@ ( esk54_0
@ ^ [Z5: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( esk54_0
@ ^ [Z6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: ( $i > $i ) > $i,Z8: $i > $i] : c_Empty
@ c_Empty ) )
@ ^ [Z5: $i,Z6: ( $i > $i ) > $i,Z7: $i > $i] :
( esk54_0
@ ^ [Z8: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( Z6
@ ^ [Z9: $i] : c_Empty )
@ ^ [Z8: $i,Z9: ( $i > $i ) > $i,Z10: $i > $i] :
( esk54_0
@ ^ [Z11: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z11: $i,Z12: ( $i > $i ) > $i,Z13: $i > $i] : c_Empty
@ c_Empty )
@ ( Z6
@ ^ [Z8: $i] : c_Empty ) )
@ ( c_Inj0 @ ( Z3 @ c_Empty ) ) )
@ Z1 )
@ ^ [Z0: $i > ( $i > $i ) > $i] :
( Z0 @ c_Empty
@ ^ [Z1: $i] : c_Empty ) )
= ( X1115
@ ^ [Z0: ( $i > $i ) > $i > $i,Z1: $i,Z2: $i] :
( esk53_0
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z4: $i,Z5: $i,Z6: $i > $i,Z7: $i] :
( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( esk55_0
@ ^ [Z8: ( ( $i > $i > $i ) > $i > $i ) > $i,Z9: $i > $i > $i] :
( esk54_0
@ ^ [Z10: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z10: $i,Z11: ( $i > $i ) > $i,Z12: $i > $i] : c_Empty
@ c_Empty )
@ ( c_Inj1 @ c_Empty ) ) )
@ ^ [Z3: $i > ( $i > $i ) > $i] :
( esk55_0
@ ^ [Z4: ( ( $i > $i > $i ) > $i > $i ) > $i,Z5: $i > $i > $i] :
( c_setsum
@ ( Z4
@ ^ [Z6: $i > $i > $i,Z7: $i] : c_Empty )
@ ( c_setsum @ c_Empty @ c_Empty ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) ) ) )
@ ( esk55_0
@ ^ [Z0: ( ( $i > $i > $i ) > $i > $i ) > $i,Z1: $i > $i > $i] :
( esk52_0
@ ^ [Z2: $i] :
( Z0
@ ^ [Z3: $i > $i > $i,Z4: $i] :
( esk53_0
@ ^ [Z5: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z6: $i,Z7: $i,Z8: $i > $i,Z9: $i] : c_Empty
@ ^ [Z5: $i > ( $i > $i ) > $i] : c_Empty ) )
@ ^ [Z2: $i,Z3: $i,Z4: $i > $i] :
( esk52_0
@ ^ [Z5: $i] :
( esk52_0
@ ^ [Z6: $i] : c_Empty
@ ^ [Z6: $i,Z7: $i,Z8: $i > $i] : c_Empty )
@ ^ [Z5: $i,Z6: $i,Z7: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( c_setsum @ ( c_Inj1 @ c_Empty )
@ ( X1117
@ ( X1118 @ c_Empty
@ ^ [Z0: $i > $i] : c_Empty
@ ^ [Z0: $i] : c_Empty
@ c_Empty ) ) ) )
@ ( X1116
@ ^ [Z0: $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
& ( ( esk52_0
@ ^ [Z0: $i] :
( esk55_0
@ ^ [Z1: ( ( $i > $i > $i ) > $i > $i ) > $i,Z2: $i > $i > $i] : c_Empty
@ ( c_setsum @ c_Empty
@ ( c_Inj0
@ ( esk54_0
@ ^ [Z1: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z1: $i,Z2: ( $i > $i ) > $i,Z3: $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( esk54_0
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z3: $i,Z4: ( $i > $i ) > $i,Z5: $i > $i] :
( c_setsum
@ ( esk54_0
@ ^ [Z6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: ( $i > $i ) > $i,Z8: $i > $i] : c_Empty
@ ( Z4
@ ^ [Z6: $i] : c_Empty ) )
@ ( c_Inj1
@ ( esk53_0
@ ^ [Z6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z7: $i,Z8: $i,Z9: $i > $i,Z10: $i] : c_Empty
@ ^ [Z6: $i > ( $i > $i ) > $i] : c_Empty ) ) )
@ c_Empty ) )
= ( esk54_0
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] :
( c_setsum
@ ( Z0 @ c_Empty
@ ^ [Z1: $i > $i,Z2: $i] : ( c_Inj1 @ ( c_Inj0 @ c_Empty ) )
@ ( c_setsum @ c_Empty
@ ( esk55_0
@ ^ [Z1: ( ( $i > $i > $i ) > $i > $i ) > $i,Z2: $i > $i > $i] : c_Empty
@ c_Empty ) )
@ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) )
@ ( esk53_0
@ ^ [Z1: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,Z2: $i,Z3: $i,Z4: $i > $i,Z5: $i] : ( c_Inj0 @ c_Empty )
@ ^ [Z1: $i > ( $i > $i ) > $i] :
( c_Inj1
@ ( esk55_0
@ ^ [Z2: ( ( $i > $i > $i ) > $i > $i ) > $i,Z3: $i > $i > $i] : c_Empty
@ c_Empty ) ) ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] :
( c_setsum
@ ( esk54_0
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z3: $i,Z4: ( $i > $i ) > $i,Z5: $i > $i] :
( c_Inj1
@ ( esk54_0
@ ^ [Z6: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z6: $i,Z7: ( $i > $i ) > $i,Z8: $i > $i] : c_Empty
@ c_Empty ) )
@ ( X1120
@ ^ [Z3: $i,Z4: $i > $i] : ( c_setsum @ c_Empty @ c_Empty )
@ ( esk54_0
@ ^ [Z3: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : c_Empty
@ ^ [Z3: $i,Z4: ( $i > $i ) > $i,Z5: $i > $i] : c_Empty
@ c_Empty )
@ ^ [Z3: $i] : Z0 ) )
@ ( Z1
@ ^ [Z3: $i] :
( c_Inj1
@ ( esk52_0
@ ^ [Z4: $i] : c_Empty
@ ^ [Z4: $i,Z5: $i,Z6: $i > $i] : c_Empty ) ) ) )
@ ( esk54_0
@ ^ [Z0: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i] : ( X1119 @ ( X1119 @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ^ [Z0: $i,Z1: ( $i > $i ) > $i,Z2: $i > $i] : c_Empty
@ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
& ( ( esk52_0
@ ^ [Z0: $i] : Z0
@ ^ [Z0: $i,Z1: $i,Z2: $i > $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ c_Empty ) ) )
= ( c_Inj0 @ c_Empty ) )
& ~ 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_11])])])])])]) ).
thf(c_0_17,plain,
! [X2401: $i > ( $i > $i ) > $i,X323: ( $i > $i > $i > $i ) > $i] :
( ( esk264_1 @ X323 @ X2401 )
= ( c_setsum @ c_Empty @ ( c_setsum @ ( X323 @ ( esk263_0 @ X2401 ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ ( X2401 @ c_Empty @ ( esk221_1 @ c_Empty ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_18,plain,
! [X2222: $i,X6: $i] :
( ( esk221_1 @ X6 @ X2222 )
= X6 ),
introduced(definition) ).
thf(c_0_19,plain,
! [X2398: $i,X2397: $i,X2396: $i,X2399: $i > ( $i > $i ) > $i] :
( ( esk263_0 @ X2399 @ X2396 @ X2397 @ X2398 )
= ( X2399 @ c_Empty @ ( esk221_1 @ c_Empty ) ) ),
introduced(definition) ).
thf(c_0_20,plain,
! [X2394: $i,X2393: $i > $i,X2392: $i,X2391: $i,X2390: $i > ( ( $i > $i ) > $i > $i ) > $i > $i] :
( ( esk262_0 @ X2390 @ X2391 @ X2392 @ X2393 @ X2394 )
= X2391 ),
introduced(definition) ).
thf(c_0_21,plain,
! [X744: $i,X745: $i] :
( ( ~ ( c_Subq @ X745 @ X744 )
| ( c_iff @ $true @ $true )
| ~ ( c_In @ X745 @ ( c_Power @ X744 ) ) )
& ( ( c_Subq @ X745 @ X744 )
| ( c_iff @ $true @ $false )
| ~ ( c_In @ X745 @ ( c_Power @ X744 ) ) )
& ( ~ ( c_Subq @ X745 @ X744 )
| ( c_iff @ $false @ $true )
| ( c_In @ X745 @ ( c_Power @ X744 ) ) )
& ( ( c_Subq @ X745 @ X744 )
| ( c_iff @ $false @ $false )
| ( c_In @ X745 @ ( c_Power @ X744 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])])]) ).
thf(c_0_22,plain,
! [X732: $o,X733: $o] :
( ( ~ X732
| X733
| ~ ( c_iff @ X732 @ X733 ) )
& ( ~ X733
| X732
| ~ ( c_iff @ X732 @ X733 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).
thf(c_0_23,plain,
! [X2: $i] :
( ( c_not @ $true )
| ~ ( c_In @ X2 @ c_Empty ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_24,plain,
~ ( c_not @ $true ),
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_25,negated_conjecture,
! [X323: ( $i > $i > $i > $i ) > $i,X2: $i] :
( ( esk53_0 @ esk262_0 @ ( esk264_1 @ X323 ) )
= X2 ),
inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_18]),c_0_20]) ).
thf(c_0_26,plain,
! [X528: $i,X529: $i] :
( ( c_Subq @ X528 @ X529 )
<=> ! [X9: $i] :
( ( c_In @ X9 @ X528 )
=> ( c_In @ X9 @ X529 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax17])]) ).
thf(c_0_27,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_21]) ).
thf(c_0_28,plain,
~ ( c_iff @ ~ $true @ $true ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_22])])]) ).
thf(c_0_29,plain,
! [X2: $i] :
~ ( c_In @ X2 @ c_Empty ),
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i,X6: $i] : ( X2 = X6 ),
inference(spm,[status(thm)],[c_0_25,c_0_25]) ).
thf(c_0_31,plain,
! [X784: $i,X785: $i,X786: $i,X787: $i,X788: $i] :
( ( ~ ( c_Subq @ X784 @ X785 )
| ~ ( c_In @ X786 @ X784 )
| ( c_In @ X786 @ X785 ) )
& ( ( c_In @ ( esk13_2 @ X787 @ X788 ) @ X787 )
| ( c_Subq @ X787 @ X788 ) )
& ( ~ ( c_In @ ( esk13_2 @ X787 @ X788 ) @ X788 )
| ( c_Subq @ X787 @ X788 ) ) ),
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_26])])])])])])]) ).
thf(c_0_32,plain,
! [X2: $i,X6: $i] :
( ( c_In @ X2 @ ( c_Power @ X6 ) )
| ~ ( c_Subq @ X2 @ X6 ) ),
inference(sr,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_33,negated_conjecture,
! [X2: $i,X6: $i] :
~ ( c_In @ X2 @ X6 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_34,plain,
! [X2: $i,X6: $i] :
( ( c_In @ ( esk13_2 @ X2 @ X6 ) @ X2 )
| ( c_Subq @ X2 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_35,plain,
! [X2: $i,X6: $i] :
~ ( c_Subq @ X2 @ X6 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_30]),c_0_33]) ).
thf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_30]),c_0_33]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO854^1 : TPTP v8.2.0. Released v7.5.0.
% 0.10/0.14 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon May 20 08:59:53 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.18/0.46 Running higher-order theorem proving
% 0.18/0.46 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
% 54.70/18.23 # Version: 3.1.0-ho
% 54.70/18.23 # partial match(2): HSLMSMSSSSLCHSA
% 54.70/18.23 # Preprocessing class: HSLMSLSSSSLCHHA.
% 54.70/18.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 54.70/18.23 # Starting pre_casc_6 with 1500s (5) cores
% 54.70/18.23 # Starting ehoh_best7 with 300s (1) cores
% 54.70/18.23 # Starting new_bool_8 with 300s (1) cores
% 54.70/18.23 # Starting new_ho_11 with 300s (1) cores
% 54.70/18.23 # new_bool_8 with pid 11691 completed with status 8
% 54.70/18.23 # new_ho_11 with pid 11692 completed with status 0
% 54.70/18.23 # Result found by new_ho_11
% 54.70/18.23 # partial match(2): HSLMSMSSSSLCHSA
% 54.70/18.23 # Preprocessing class: HSLMSLSSSSLCHHA.
% 54.70/18.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 54.70/18.23 # Starting pre_casc_6 with 1500s (5) cores
% 54.70/18.23 # Starting ehoh_best7 with 300s (1) cores
% 54.70/18.23 # Starting new_bool_8 with 300s (1) cores
% 54.70/18.23 # Starting new_ho_11 with 300s (1) cores
% 54.70/18.23 # No SInE strategy applied
% 54.70/18.23 # Search class: HGHSM-SMLM33-DHHFFSBC
% 54.70/18.23 # partial match(2): HGHSM-SMLM33-MHFFFSBC
% 54.70/18.23 # Scheduled 6 strats onto 1 cores with 284 seconds (284 total)
% 54.70/18.23 # Starting new_ho_10 with 154s (1) cores
% 54.70/18.23 # new_ho_10 with pid 11941 completed with status 0
% 54.70/18.23 # Result found by new_ho_10
% 54.70/18.23 # partial match(2): HSLMSMSSSSLCHSA
% 54.70/18.23 # Preprocessing class: HSLMSLSSSSLCHHA.
% 54.70/18.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 54.70/18.23 # Starting pre_casc_6 with 1500s (5) cores
% 54.70/18.23 # Starting ehoh_best7 with 300s (1) cores
% 54.70/18.23 # Starting new_bool_8 with 300s (1) cores
% 54.70/18.23 # Starting new_ho_11 with 300s (1) cores
% 54.70/18.23 # No SInE strategy applied
% 54.70/18.23 # Search class: HGHSM-SMLM33-DHHFFSBC
% 54.70/18.23 # partial match(2): HGHSM-SMLM33-MHFFFSBC
% 54.70/18.23 # Scheduled 6 strats onto 1 cores with 284 seconds (284 total)
% 54.70/18.23 # Starting new_ho_10 with 154s (1) cores
% 54.70/18.23 # Preprocessing time : 0.141 s
% 54.70/18.23 # Presaturation interreduction done
% 54.70/18.23
% 54.70/18.23 # Proof found!
% 54.70/18.23 # SZS status Theorem
% 54.70/18.23 # SZS output start CNFRefutation
% See solution above
% 54.70/18.23 # Parsed axioms : 213
% 54.70/18.23 # Removed by relevancy pruning/SinE : 0
% 54.70/18.23 # Initial clauses : 468753
% 54.70/18.23 # Removed in clause preprocessing : 463862
% 54.70/18.23 # Initial clauses in saturation : 4891
% 54.70/18.23 # Processed clauses : 5685
% 54.70/18.23 # ...of these trivial : 285
% 54.70/18.23 # ...subsumed : 3424
% 54.70/18.23 # ...remaining for further processing : 1975
% 54.70/18.23 # Other redundant clauses eliminated : 73
% 54.70/18.23 # Clauses deleted for lack of memory : 0
% 54.70/18.23 # Backward-subsumed : 303
% 54.70/18.23 # Backward-rewritten : 169
% 54.70/18.23 # Generated clauses : 699
% 54.70/18.23 # ...of the previous two non-redundant : 588
% 54.70/18.23 # ...aggressively subsumed : 0
% 54.70/18.23 # Contextual simplify-reflections : 229
% 54.70/18.23 # Paramodulations : 630
% 54.70/18.23 # Factorizations : 0
% 54.70/18.23 # NegExts : 0
% 54.70/18.23 # Equation resolutions : 73
% 54.70/18.23 # Disequality decompositions : 0
% 54.70/18.23 # Total rewrite steps : 4204
% 54.70/18.23 # ...of those cached : 3563
% 54.70/18.23 # Propositional unsat checks : 0
% 54.70/18.23 # Propositional check models : 0
% 54.70/18.23 # Propositional check unsatisfiable : 0
% 54.70/18.23 # Propositional clauses : 0
% 54.70/18.23 # Propositional clauses after purity: 0
% 54.70/18.23 # Propositional unsat core size : 0
% 54.70/18.23 # Propositional preprocessing time : 0.000
% 54.70/18.23 # Propositional encoding time : 0.000
% 54.70/18.23 # Propositional solver time : 0.000
% 54.70/18.23 # Success case prop preproc time : 0.000
% 54.70/18.23 # Success case prop encoding time : 0.000
% 54.70/18.23 # Success case prop solver time : 0.000
% 54.70/18.23 # Current number of processed clauses : 307
% 54.70/18.23 # Positive orientable unit clauses : 58
% 54.70/18.23 # Positive unorientable unit clauses: 4
% 54.70/18.23 # Negative unit clauses : 29
% 54.70/18.23 # Non-unit-clauses : 216
% 54.70/18.23 # Current number of unprocessed clauses: 767
% 54.70/18.23 # ...number of literals in the above : 2749
% 54.70/18.23 # Current number of archived formulas : 0
% 54.70/18.23 # Current number of archived clauses : 1608
% 54.70/18.23 # Clause-clause subsumption calls (NU) : 763063
% 54.70/18.23 # Rec. Clause-clause subsumption calls : 184679
% 54.70/18.23 # Non-unit clause-clause subsumptions : 1546
% 54.70/18.23 # Unit Clause-clause subsumption calls : 8869
% 54.70/18.23 # Rewrite failures with RHS unbound : 0
% 54.70/18.23 # BW rewrite match attempts : 1987
% 54.70/18.23 # BW rewrite match successes : 196
% 54.70/18.23 # Condensation attempts : 5743
% 54.70/18.23 # Condensation successes : 215
% 54.70/18.23 # Termbank termtop insertions : 20103413
% 54.70/18.23 # Search garbage collected termcells : 2012549
% 54.70/18.23
% 54.70/18.23 # -------------------------------------------------
% 54.70/18.23 # User time : 16.524 s
% 54.70/18.23 # System time : 0.924 s
% 54.70/18.23 # Total time : 17.447 s
% 54.70/18.23 # Maximum resident set size: 1256952 pages
% 54.70/18.23
% 54.70/18.23 # -------------------------------------------------
% 54.70/18.23 # User time : 16.687 s
% 54.70/18.23 # System time : 1.140 s
% 54.70/18.23 # Total time : 17.827 s
% 54.70/18.23 # Maximum resident set size: 2336 pages
% 54.70/18.23 % E---3.1 exiting
% 54.70/18.23 % E exiting
%------------------------------------------------------------------------------