TSTP Solution File: NUM505+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM505+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 02:04:36 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 68
% Syntax : Number of formulae : 476 ( 137 unt; 0 def)
% Number of atoms : 1843 ( 694 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 2218 ( 851 ~; 834 |; 431 &)
% ( 17 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 13 con; 0-2 aty)
% Number of variables : 720 ( 634 !; 86 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f608,plain,
$false,
inference(global_subsumption,[],[f201,f200,f222,f221,f233,f232,f254,f253,f252,f251,f266,f268,f267,f277,f276,f275,f274,f273,f281,f280,f279,f284,f285,f338,f288,f330,f331,f332,f293,f292,f294,f295,f299,f298,f297,f296,f300,f333,f334,f335,f304,f305,f336,f307,f306,f337,f310,f309,f312,f313,f315,f314,f319,f318,f339,f317,f316,f340,f320,f321,f322,f323,f325,f324,f194,f195,f202,f203,f204,f205,f206,f210,f214,f223,f224,f227,f229,f255,f256,f327,f328,f191,f197,f198,f199,f209,f212,f213,f216,f217,f218,f219,f220,f235,f237,f257,f278,f193,f196,f211,f215,f226,f228,f231,f244,f258,f190,f240,f243,f245,f246,f247,f248,f269,f270,f350,f354,f355,f351,f207,f208,f225,f230,f234,f236,f238,f241,f249,f259,f371,f372,f374,f360,f361,f362,f260,f375,f388,f389,f391,f363,f364,f365,f366,f367,f368,f369,f370,f377,f378,f379,f261,f405,f406,f408,f380,f381,f382,f383,f384,f385,f386,f387,f394,f395,f396,f262,f412,f425,f426,f428,f397,f398,f399,f400,f401,f402,f403,f404,f414,f415,f416,f263,f429,f442,f443,f445,f417,f418,f419,f420,f421,f422,f423,f424,f431,f432,f433,f264,f446,f447,f459,f460,f462,f434,f435,f436,f437,f438,f439,f440,f441,f448,f449,f450,f451,f452,f453,f454,f455,f456,f457,f458,f358,f359,f376,f392,f393,f413,f430,f282,f465,f466,f467,f468,f469,f470,f283,f500,f501,f502,f503,f504,f505,f563,f565,f239,f561,f570,f571,f373,f390,f407,f427,f444,f461,f242,f566,f567,f568,f569,f250,f578,f287,f192,f605,f607]) ).
fof(f607,plain,
sdtlseqdt0(xk,xp),
inference(subsumption_resolution,[],[f606,f205]) ).
fof(f606,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f583,f206]) ).
fof(f583,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f287,f191]) ).
fof(f605,plain,
xp != xk,
inference(subsumption_resolution,[],[f411,f255]) ).
fof(f411,plain,
( xp != xk
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[],[f190,f396]) ).
fof(f192,plain,
! [X0] :
( xp != sdtpldt0(xk,X0)
| ~ aNaturalNumber0(X0)
| xp = xk ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ( ( ~ sdtlseqdt0(xk,xp)
& ! [X0] :
( xp != sdtpldt0(xk,X0)
| ~ aNaturalNumber0(X0) ) )
| xp = xk )
& ~ sdtlseqdt0(xp,xk)
& ! [X1] :
( xk != sdtpldt0(xp,X1)
| ~ aNaturalNumber0(X1) ) ),
inference(rectify,[],[f61]) ).
fof(f61,plain,
( ( ( ~ sdtlseqdt0(xk,xp)
& ! [X1] :
( xp != sdtpldt0(xk,X1)
| ~ aNaturalNumber0(X1) ) )
| xp = xk )
& ~ sdtlseqdt0(xp,xk)
& ! [X0] :
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(X0) ) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
( ( ( ~ sdtlseqdt0(xk,xp)
& ! [X1] :
( xp != sdtpldt0(xk,X1)
| ~ aNaturalNumber0(X1) ) )
| xp = xk )
& ~ sdtlseqdt0(xp,xk)
& ! [X0] :
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
~ ( ~ ( sdtlseqdt0(xp,xk)
| ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [X1] :
( xp = sdtpldt0(xk,X1)
& aNaturalNumber0(X1) ) )
& xp != xk ) ),
inference(rectify,[],[f51]) ).
fof(f51,negated_conjecture,
~ ( ~ ( sdtlseqdt0(xp,xk)
| ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [X0] :
( xp = sdtpldt0(xk,X0)
& aNaturalNumber0(X0) ) )
& xp != xk ) ),
inference(negated_conjecture,[],[f50]) ).
fof(f50,conjecture,
( ~ ( sdtlseqdt0(xp,xk)
| ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [X0] :
( xp = sdtpldt0(xk,X0)
& aNaturalNumber0(X0) ) )
& xp != xk ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f287,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f578,plain,
! [X0] :
( sdtasdt0(sK14(X0),sK15(X0,sK14(X0))) = X0
| ~ sP1(X0) ),
inference(resolution,[],[f250,f245]) ).
fof(f250,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sdtasdt0(X1,sK15(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f169]) ).
fof(f169,plain,
! [X0,X1] :
( ( sdtasdt0(X1,sK15(X0,X1)) = X0
& aNaturalNumber0(sK15(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f167,f168]) ).
fof(f168,plain,
! [X0,X1] :
( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,sK15(X0,X1)) = X0
& aNaturalNumber0(sK15(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f167,plain,
! [X0,X1] :
( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f166]) ).
fof(f166,plain,
! [X2,X4] :
( ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
| ~ sP0(X2,X4) ),
inference(nnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X2,X4] :
( ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
| ~ sP0(X2,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f569,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xn,xm),sz00),
inference(resolution,[],[f561,f261]) ).
fof(f568,plain,
sdtasdt0(xn,xm) = sdtpldt0(sz00,sdtasdt0(xn,xm)),
inference(resolution,[],[f561,f262]) ).
fof(f567,plain,
sdtasdt0(xn,xm) = sdtasdt0(sdtasdt0(xn,xm),sz10),
inference(resolution,[],[f561,f263]) ).
fof(f566,plain,
sdtasdt0(xn,xm) = sdtasdt0(sz10,sdtasdt0(xn,xm)),
inference(resolution,[],[f561,f264]) ).
fof(f242,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sdtasdt0(X1,sK13(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& sdtasdt0(X1,sK13(X0,X1)) = X0
& aNaturalNumber0(sK13(X0,X1)) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f159,f160]) ).
fof(f160,plain,
! [X0,X1] :
( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,sK13(X0,X1)) = X0
& aNaturalNumber0(sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) ) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f158]) ).
fof(f158,plain,
! [X0,X2] :
( ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ sP2(X0,X2) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X2] :
( ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ sP2(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f461,plain,
! [X0] :
( ~ sP1(X0)
| sK14(X0) = sdtasdt0(sz10,sK14(X0)) ),
inference(resolution,[],[f264,f244]) ).
fof(f444,plain,
! [X0] :
( ~ sP1(X0)
| sK14(X0) = sdtasdt0(sK14(X0),sz10) ),
inference(resolution,[],[f263,f244]) ).
fof(f427,plain,
! [X0] :
( ~ sP1(X0)
| sK14(X0) = sdtpldt0(sz00,sK14(X0)) ),
inference(resolution,[],[f262,f244]) ).
fof(f407,plain,
! [X0] :
( ~ sP1(X0)
| sK14(X0) = sdtpldt0(sK14(X0),sz00) ),
inference(resolution,[],[f261,f244]) ).
fof(f390,plain,
! [X0] :
( ~ sP1(X0)
| sz00 = sdtasdt0(sz00,sK14(X0)) ),
inference(resolution,[],[f260,f244]) ).
fof(f373,plain,
! [X0] :
( ~ sP1(X0)
| sz00 = sdtasdt0(sK14(X0),sz00) ),
inference(resolution,[],[f259,f244]) ).
fof(f571,plain,
sz00 = sdtasdt0(sdtasdt0(xn,xm),sz00),
inference(resolution,[],[f561,f259]) ).
fof(f570,plain,
sz00 = sdtasdt0(sz00,sdtasdt0(xn,xm)),
inference(resolution,[],[f561,f260]) ).
fof(f561,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(subsumption_resolution,[],[f560,f205]) ).
fof(f560,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f538,f206]) ).
fof(f538,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f283,f207]) ).
fof(f239,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sdtasdt0(X1,sK12(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& sdtasdt0(X1,sK12(X0,X1)) = X0
& aNaturalNumber0(sK12(X0,X1)) )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f155,f156]) ).
fof(f156,plain,
! [X0,X1] :
( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,sK12(X0,X1)) = X0
& aNaturalNumber0(sK12(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f155,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f154]) ).
fof(f154,plain,
! [X1,X2] :
( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| ~ sP3(X1,X2) ),
inference(nnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X1,X2] :
( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| ~ sP3(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f565,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(subsumption_resolution,[],[f564,f194]) ).
fof(f564,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr) ),
inference(subsumption_resolution,[],[f545,f229]) ).
fof(f545,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK10)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[],[f283,f230]) ).
fof(f563,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(subsumption_resolution,[],[f562,f205]) ).
fof(f562,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f539,f224]) ).
fof(f539,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK9)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f283,f225]) ).
fof(f505,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sdtasdt0(X1,X0),sz00) ),
inference(resolution,[],[f283,f259]) ).
fof(f504,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,sdtasdt0(X1,X0)) ),
inference(resolution,[],[f283,f260]) ).
fof(f503,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtpldt0(sdtasdt0(X1,X0),sz00) ),
inference(resolution,[],[f283,f261]) ).
fof(f502,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtpldt0(sz00,sdtasdt0(X1,X0)) ),
inference(resolution,[],[f283,f262]) ).
fof(f501,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtasdt0(sdtasdt0(X1,X0),sz10) ),
inference(resolution,[],[f283,f263]) ).
fof(f500,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) = sdtasdt0(sz10,sdtasdt0(X1,X0)) ),
inference(resolution,[],[f283,f264]) ).
fof(f283,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f470,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sdtpldt0(X1,X0),sz00) ),
inference(resolution,[],[f282,f259]) ).
fof(f469,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,sdtpldt0(X1,X0)) ),
inference(resolution,[],[f282,f260]) ).
fof(f468,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtpldt0(sdtpldt0(X1,X0),sz00) ),
inference(resolution,[],[f282,f261]) ).
fof(f467,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtpldt0(sz00,sdtpldt0(X1,X0)) ),
inference(resolution,[],[f282,f262]) ).
fof(f466,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtasdt0(sdtpldt0(X1,X0),sz10) ),
inference(resolution,[],[f282,f263]) ).
fof(f465,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X0) = sdtasdt0(sz10,sdtpldt0(X1,X0)) ),
inference(resolution,[],[f282,f264]) ).
fof(f282,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f430,plain,
sz10 = sdtasdt0(sz10,sz10),
inference(resolution,[],[f263,f256]) ).
fof(f413,plain,
sz10 = sdtpldt0(sz00,sz10),
inference(resolution,[],[f262,f256]) ).
fof(f393,plain,
sz10 = sdtpldt0(sz10,sz00),
inference(resolution,[],[f261,f256]) ).
fof(f392,plain,
sz00 = sdtpldt0(sz00,sz00),
inference(resolution,[],[f261,f255]) ).
fof(f376,plain,
sz00 = sdtasdt0(sz00,sz10),
inference(resolution,[],[f260,f256]) ).
fof(f359,plain,
sz00 = sdtasdt0(sz10,sz00),
inference(resolution,[],[f259,f256]) ).
fof(f358,plain,
sz00 = sdtasdt0(sz00,sz00),
inference(resolution,[],[f259,f255]) ).
fof(f458,plain,
sK11 = sdtasdt0(sz10,sK11),
inference(resolution,[],[f264,f227]) ).
fof(f457,plain,
sK10 = sdtasdt0(sz10,sK10),
inference(resolution,[],[f264,f229]) ).
fof(f456,plain,
sK9 = sdtasdt0(sz10,sK9),
inference(resolution,[],[f264,f224]) ).
fof(f455,plain,
sK8 = sdtasdt0(sz10,sK8),
inference(resolution,[],[f264,f210]) ).
fof(f454,plain,
sK7 = sdtasdt0(sz10,sK7),
inference(resolution,[],[f264,f214]) ).
fof(f453,plain,
sK6 = sdtasdt0(sz10,sK6),
inference(resolution,[],[f264,f195]) ).
fof(f452,plain,
xr = sdtasdt0(sz10,xr),
inference(resolution,[],[f264,f194]) ).
fof(f451,plain,
xk = sdtasdt0(sz10,xk),
inference(resolution,[],[f264,f206]) ).
fof(f450,plain,
xp = sdtasdt0(sz10,xp),
inference(resolution,[],[f264,f205]) ).
fof(f449,plain,
xm = sdtasdt0(sz10,xm),
inference(resolution,[],[f264,f204]) ).
fof(f448,plain,
xn = sdtasdt0(sz10,xn),
inference(resolution,[],[f264,f203]) ).
fof(f441,plain,
sK11 = sdtasdt0(sK11,sz10),
inference(resolution,[],[f263,f227]) ).
fof(f440,plain,
sK10 = sdtasdt0(sK10,sz10),
inference(resolution,[],[f263,f229]) ).
fof(f439,plain,
sK9 = sdtasdt0(sK9,sz10),
inference(resolution,[],[f263,f224]) ).
fof(f438,plain,
sK8 = sdtasdt0(sK8,sz10),
inference(resolution,[],[f263,f210]) ).
fof(f437,plain,
sK7 = sdtasdt0(sK7,sz10),
inference(resolution,[],[f263,f214]) ).
fof(f436,plain,
sK6 = sdtasdt0(sK6,sz10),
inference(resolution,[],[f263,f195]) ).
fof(f435,plain,
xr = sdtasdt0(xr,sz10),
inference(resolution,[],[f263,f194]) ).
fof(f434,plain,
xk = sdtasdt0(xk,sz10),
inference(resolution,[],[f263,f206]) ).
fof(f462,plain,
! [X0,X1] :
( sK15(X0,X1) = sdtasdt0(sz10,sK15(X0,X1))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f264,f249]) ).
fof(f460,plain,
! [X0,X1] :
( sK13(X0,X1) = sdtasdt0(sz10,sK13(X0,X1))
| ~ sP2(X0,X1) ),
inference(resolution,[],[f264,f241]) ).
fof(f459,plain,
! [X0,X1] :
( sK12(X0,X1) = sdtasdt0(sz10,sK12(X0,X1))
| ~ sP3(X0,X1) ),
inference(resolution,[],[f264,f238]) ).
fof(f447,plain,
sz10 = sdtasdt0(sz10,sz10),
inference(resolution,[],[f264,f256]) ).
fof(f446,plain,
sz00 = sdtasdt0(sz10,sz00),
inference(resolution,[],[f264,f255]) ).
fof(f264,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f433,plain,
xp = sdtasdt0(xp,sz10),
inference(resolution,[],[f263,f205]) ).
fof(f432,plain,
xm = sdtasdt0(xm,sz10),
inference(resolution,[],[f263,f204]) ).
fof(f431,plain,
xn = sdtasdt0(xn,sz10),
inference(resolution,[],[f263,f203]) ).
fof(f424,plain,
sK11 = sdtpldt0(sz00,sK11),
inference(resolution,[],[f262,f227]) ).
fof(f423,plain,
sK10 = sdtpldt0(sz00,sK10),
inference(resolution,[],[f262,f229]) ).
fof(f422,plain,
sK9 = sdtpldt0(sz00,sK9),
inference(resolution,[],[f262,f224]) ).
fof(f421,plain,
sK8 = sdtpldt0(sz00,sK8),
inference(resolution,[],[f262,f210]) ).
fof(f420,plain,
sK7 = sdtpldt0(sz00,sK7),
inference(resolution,[],[f262,f214]) ).
fof(f419,plain,
sK6 = sdtpldt0(sz00,sK6),
inference(resolution,[],[f262,f195]) ).
fof(f418,plain,
xr = sdtpldt0(sz00,xr),
inference(resolution,[],[f262,f194]) ).
fof(f417,plain,
xk = sdtpldt0(sz00,xk),
inference(resolution,[],[f262,f206]) ).
fof(f445,plain,
! [X0,X1] :
( sK15(X0,X1) = sdtasdt0(sK15(X0,X1),sz10)
| ~ sP0(X0,X1) ),
inference(resolution,[],[f263,f249]) ).
fof(f443,plain,
! [X0,X1] :
( sK13(X0,X1) = sdtasdt0(sK13(X0,X1),sz10)
| ~ sP2(X0,X1) ),
inference(resolution,[],[f263,f241]) ).
fof(f442,plain,
! [X0,X1] :
( sK12(X0,X1) = sdtasdt0(sK12(X0,X1),sz10)
| ~ sP3(X0,X1) ),
inference(resolution,[],[f263,f238]) ).
fof(f429,plain,
sz00 = sdtasdt0(sz00,sz10),
inference(resolution,[],[f263,f255]) ).
fof(f263,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f416,plain,
xp = sdtpldt0(sz00,xp),
inference(resolution,[],[f262,f205]) ).
fof(f415,plain,
xm = sdtpldt0(sz00,xm),
inference(resolution,[],[f262,f204]) ).
fof(f414,plain,
xn = sdtpldt0(sz00,xn),
inference(resolution,[],[f262,f203]) ).
fof(f404,plain,
sK11 = sdtpldt0(sK11,sz00),
inference(resolution,[],[f261,f227]) ).
fof(f403,plain,
sK10 = sdtpldt0(sK10,sz00),
inference(resolution,[],[f261,f229]) ).
fof(f402,plain,
sK9 = sdtpldt0(sK9,sz00),
inference(resolution,[],[f261,f224]) ).
fof(f401,plain,
sK8 = sdtpldt0(sK8,sz00),
inference(resolution,[],[f261,f210]) ).
fof(f400,plain,
sK7 = sdtpldt0(sK7,sz00),
inference(resolution,[],[f261,f214]) ).
fof(f399,plain,
sK6 = sdtpldt0(sK6,sz00),
inference(resolution,[],[f261,f195]) ).
fof(f398,plain,
xr = sdtpldt0(xr,sz00),
inference(resolution,[],[f261,f194]) ).
fof(f397,plain,
xk = sdtpldt0(xk,sz00),
inference(resolution,[],[f261,f206]) ).
fof(f428,plain,
! [X0,X1] :
( sK15(X0,X1) = sdtpldt0(sz00,sK15(X0,X1))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f262,f249]) ).
fof(f426,plain,
! [X0,X1] :
( sK13(X0,X1) = sdtpldt0(sz00,sK13(X0,X1))
| ~ sP2(X0,X1) ),
inference(resolution,[],[f262,f241]) ).
fof(f425,plain,
! [X0,X1] :
( sK12(X0,X1) = sdtpldt0(sz00,sK12(X0,X1))
| ~ sP3(X0,X1) ),
inference(resolution,[],[f262,f238]) ).
fof(f412,plain,
sz00 = sdtpldt0(sz00,sz00),
inference(resolution,[],[f262,f255]) ).
fof(f262,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f396,plain,
xp = sdtpldt0(xp,sz00),
inference(resolution,[],[f261,f205]) ).
fof(f395,plain,
xm = sdtpldt0(xm,sz00),
inference(resolution,[],[f261,f204]) ).
fof(f394,plain,
xn = sdtpldt0(xn,sz00),
inference(resolution,[],[f261,f203]) ).
fof(f387,plain,
sz00 = sdtasdt0(sz00,sK11),
inference(resolution,[],[f260,f227]) ).
fof(f386,plain,
sz00 = sdtasdt0(sz00,sK10),
inference(resolution,[],[f260,f229]) ).
fof(f385,plain,
sz00 = sdtasdt0(sz00,sK9),
inference(resolution,[],[f260,f224]) ).
fof(f384,plain,
sz00 = sdtasdt0(sz00,sK8),
inference(resolution,[],[f260,f210]) ).
fof(f383,plain,
sz00 = sdtasdt0(sz00,sK7),
inference(resolution,[],[f260,f214]) ).
fof(f382,plain,
sz00 = sdtasdt0(sz00,sK6),
inference(resolution,[],[f260,f195]) ).
fof(f381,plain,
sz00 = sdtasdt0(sz00,xr),
inference(resolution,[],[f260,f194]) ).
fof(f380,plain,
sz00 = sdtasdt0(sz00,xk),
inference(resolution,[],[f260,f206]) ).
fof(f408,plain,
! [X0,X1] :
( sK15(X0,X1) = sdtpldt0(sK15(X0,X1),sz00)
| ~ sP0(X0,X1) ),
inference(resolution,[],[f261,f249]) ).
fof(f406,plain,
! [X0,X1] :
( sK13(X0,X1) = sdtpldt0(sK13(X0,X1),sz00)
| ~ sP2(X0,X1) ),
inference(resolution,[],[f261,f241]) ).
fof(f405,plain,
! [X0,X1] :
( sK12(X0,X1) = sdtpldt0(sK12(X0,X1),sz00)
| ~ sP3(X0,X1) ),
inference(resolution,[],[f261,f238]) ).
fof(f261,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f73]) ).
fof(f379,plain,
sz00 = sdtasdt0(sz00,xp),
inference(resolution,[],[f260,f205]) ).
fof(f378,plain,
sz00 = sdtasdt0(sz00,xm),
inference(resolution,[],[f260,f204]) ).
fof(f377,plain,
sz00 = sdtasdt0(sz00,xn),
inference(resolution,[],[f260,f203]) ).
fof(f370,plain,
sz00 = sdtasdt0(sK11,sz00),
inference(resolution,[],[f259,f227]) ).
fof(f369,plain,
sz00 = sdtasdt0(sK10,sz00),
inference(resolution,[],[f259,f229]) ).
fof(f368,plain,
sz00 = sdtasdt0(sK9,sz00),
inference(resolution,[],[f259,f224]) ).
fof(f367,plain,
sz00 = sdtasdt0(sK8,sz00),
inference(resolution,[],[f259,f210]) ).
fof(f366,plain,
sz00 = sdtasdt0(sK7,sz00),
inference(resolution,[],[f259,f214]) ).
fof(f365,plain,
sz00 = sdtasdt0(sK6,sz00),
inference(resolution,[],[f259,f195]) ).
fof(f364,plain,
sz00 = sdtasdt0(xr,sz00),
inference(resolution,[],[f259,f194]) ).
fof(f363,plain,
sz00 = sdtasdt0(xk,sz00),
inference(resolution,[],[f259,f206]) ).
fof(f391,plain,
! [X0,X1] :
( sz00 = sdtasdt0(sz00,sK15(X0,X1))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f260,f249]) ).
fof(f389,plain,
! [X0,X1] :
( sz00 = sdtasdt0(sz00,sK13(X0,X1))
| ~ sP2(X0,X1) ),
inference(resolution,[],[f260,f241]) ).
fof(f388,plain,
! [X0,X1] :
( sz00 = sdtasdt0(sz00,sK12(X0,X1))
| ~ sP3(X0,X1) ),
inference(resolution,[],[f260,f238]) ).
fof(f375,plain,
sz00 = sdtasdt0(sz00,sz00),
inference(resolution,[],[f260,f255]) ).
fof(f260,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f362,plain,
sz00 = sdtasdt0(xp,sz00),
inference(resolution,[],[f259,f205]) ).
fof(f361,plain,
sz00 = sdtasdt0(xm,sz00),
inference(resolution,[],[f259,f204]) ).
fof(f360,plain,
sz00 = sdtasdt0(xn,sz00),
inference(resolution,[],[f259,f203]) ).
fof(f374,plain,
! [X0,X1] :
( sz00 = sdtasdt0(sK15(X0,X1),sz00)
| ~ sP0(X0,X1) ),
inference(resolution,[],[f259,f249]) ).
fof(f372,plain,
! [X0,X1] :
( sz00 = sdtasdt0(sK13(X0,X1),sz00)
| ~ sP2(X0,X1) ),
inference(resolution,[],[f259,f241]) ).
fof(f371,plain,
! [X0,X1] :
( sz00 = sdtasdt0(sK12(X0,X1),sz00)
| ~ sP3(X0,X1) ),
inference(resolution,[],[f259,f238]) ).
fof(f259,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f72]) ).
fof(f249,plain,
! [X0,X1] :
( aNaturalNumber0(sK15(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
fof(f241,plain,
! [X0,X1] :
( aNaturalNumber0(sK13(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f161]) ).
fof(f238,plain,
! [X0,X1] :
( aNaturalNumber0(sK12(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
fof(f236,plain,
! [X0] :
( xn != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
( ~ sdtlseqdt0(xp,xn)
& ! [X0] :
( xn != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
~ ( sdtlseqdt0(xp,xn)
| ? [X0] :
( xn = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(f234,plain,
! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
( ~ sdtlseqdt0(xp,xm)
& ! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
~ ( sdtlseqdt0(xp,xm)
| ? [X0] :
( xm = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(f230,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK10),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK10)
& aNaturalNumber0(sK10)
& xk = sdtpldt0(xr,sK11)
& aNaturalNumber0(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f56,f152,f151]) ).
fof(f151,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xr,sK10)
& aNaturalNumber0(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
( ? [X1] :
( xk = sdtpldt0(xr,X1)
& aNaturalNumber0(X1) )
=> ( xk = sdtpldt0(xr,sK11)
& aNaturalNumber0(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X1] :
( xk = sdtpldt0(xr,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( xk = sdtpldt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(f225,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK9),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK9)
& aNaturalNumber0(sK9)
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f65,f149]) ).
fof(f149,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK9)
& aNaturalNumber0(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( sdtasdt0(X1,X2) = xp
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xp = X1
| sz10 = X1 ) )
& sz10 != xp
& sz00 != xp ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( sdtasdt0(X0,X1) = xp
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xp = X0
| sz10 = X0 ) )
& sz10 != xp
& sz00 != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f208,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f207,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f351,plain,
! [X0] :
( ~ sP4(X0)
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f270,f278]) ).
fof(f355,plain,
~ isPrime0(sz00),
inference(subsumption_resolution,[],[f353,f255]) ).
fof(f353,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[],[f350,f328]) ).
fof(f354,plain,
~ isPrime0(sz10),
inference(subsumption_resolution,[],[f352,f256]) ).
fof(f352,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[],[f350,f327]) ).
fof(f350,plain,
! [X0] :
( sP4(X0)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f269,f278]) ).
fof(f270,plain,
! [X0] :
( ~ sP5(X0)
| ~ sP4(X0)
| isPrime0(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( ( isPrime0(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ isPrime0(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( ( isPrime0(X0)
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f269,plain,
! [X0] :
( ~ sP5(X0)
| ~ isPrime0(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f248,plain,
! [X0] :
( sK14(X0) != X0
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0] :
( ( sK14(X0) != X0
& sz10 != sK14(X0)
& doDivides0(sK14(X0),X0)
& sP0(X0,sK14(X0))
& aNaturalNumber0(sK14(X0)) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f163,f164]) ).
fof(f164,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
=> ( sK14(X0) != X0
& sz10 != sK14(X0)
& doDivides0(sK14(X0),X0)
& sP0(X0,sK14(X0))
& aNaturalNumber0(sK14(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f163,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
| ~ sP1(X0) ),
inference(rectify,[],[f162]) ).
fof(f162,plain,
! [X2] :
( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& sP0(X2,X4)
& aNaturalNumber0(X4) )
| ~ sP1(X2) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X2] :
( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& sP0(X2,X4)
& aNaturalNumber0(X4) )
| ~ sP1(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f247,plain,
! [X0] :
( sz10 != sK14(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f246,plain,
! [X0] :
( doDivides0(sK14(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f245,plain,
! [X0] :
( sP0(X0,sK14(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f243,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f240,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f190,plain,
! [X1] :
( xk != sdtpldt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f258,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
fof(f244,plain,
! [X0] :
( aNaturalNumber0(sK14(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f231,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f153]) ).
fof(f228,plain,
xk = sdtpldt0(xr,sK11),
inference(cnf_transformation,[],[f153]) ).
fof(f226,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f150]) ).
fof(f215,plain,
xp = sdtpldt0(xm,sK7),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( sdtlseqdt0(xm,xp)
& xp = sdtpldt0(xm,sK7)
& aNaturalNumber0(sK7)
& xm != xp
& sdtlseqdt0(xn,xp)
& xp = sdtpldt0(xn,sK8)
& aNaturalNumber0(sK8)
& xn != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f54,f147,f146]) ).
fof(f146,plain,
( ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
=> ( xp = sdtpldt0(xm,sK7)
& aNaturalNumber0(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
( ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
=> ( xp = sdtpldt0(xn,sK8)
& aNaturalNumber0(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& xn != xp ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( xp = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f211,plain,
xp = sdtpldt0(xn,sK8),
inference(cnf_transformation,[],[f148]) ).
fof(f196,plain,
xk = sdtasdt0(xr,sK6),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK6)
& aNaturalNumber0(sK6)
& aNaturalNumber0(xr) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f63,f144]) ).
fof(f144,plain,
( ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
=> ( xk = sdtasdt0(xr,sK6)
& aNaturalNumber0(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f193,plain,
( ~ sdtlseqdt0(xk,xp)
| xp = xk ),
inference(cnf_transformation,[],[f143]) ).
fof(f278,plain,
! [X0] :
( sP5(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( sP5(X0)
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f80,f141,f140]) ).
fof(f140,plain,
! [X0] :
( sP4(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f80,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f257,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f237,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f68]) ).
fof(f235,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f67]) ).
fof(f220,plain,
sz10 != xp,
inference(cnf_transformation,[],[f150]) ).
fof(f219,plain,
sz00 != xp,
inference(cnf_transformation,[],[f150]) ).
fof(f218,plain,
sz10 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
( sz10 != xk
& sz00 != xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
fof(f217,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f216,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f148]) ).
fof(f213,plain,
xm != xp,
inference(cnf_transformation,[],[f148]) ).
fof(f212,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f148]) ).
fof(f209,plain,
xn != xp,
inference(cnf_transformation,[],[f148]) ).
fof(f199,plain,
sz10 != xr,
inference(cnf_transformation,[],[f145]) ).
fof(f198,plain,
sz00 != xr,
inference(cnf_transformation,[],[f145]) ).
fof(f197,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f145]) ).
fof(f191,plain,
~ sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f143]) ).
fof(f328,plain,
~ sP4(sz00),
inference(equality_resolution,[],[f271]) ).
fof(f271,plain,
! [X0] :
( sz00 != X0
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ( sP4(X0)
| ( sK16(X0) != X0
& sz10 != sK16(X0)
& doDivides0(sK16(X0),X0)
& aNaturalNumber0(sK16(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f173,f174]) ).
fof(f174,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK16(X0) != X0
& sz10 != sK16(X0)
& doDivides0(sK16(X0),X0)
& aNaturalNumber0(sK16(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f173,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(rectify,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(flattening,[],[f171]) ).
fof(f171,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f140]) ).
fof(f327,plain,
~ sP4(sz10),
inference(equality_resolution,[],[f272]) ).
fof(f272,plain,
! [X0] :
( sz10 != X0
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f256,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f255,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f229,plain,
aNaturalNumber0(sK10),
inference(cnf_transformation,[],[f153]) ).
fof(f227,plain,
aNaturalNumber0(sK11),
inference(cnf_transformation,[],[f153]) ).
fof(f224,plain,
aNaturalNumber0(sK9),
inference(cnf_transformation,[],[f150]) ).
fof(f223,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f150]) ).
fof(f214,plain,
aNaturalNumber0(sK7),
inference(cnf_transformation,[],[f148]) ).
fof(f210,plain,
aNaturalNumber0(sK8),
inference(cnf_transformation,[],[f148]) ).
fof(f206,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f205,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f204,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f203,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f202,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f145]) ).
fof(f195,plain,
aNaturalNumber0(sK6),
inference(cnf_transformation,[],[f145]) ).
fof(f194,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f145]) ).
fof(f324,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f325,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f323,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f322,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,sdtpldt0(X1,X2))
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
fof(f321,plain,
! [X2,X0,X1] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(f320,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f125]) ).
fof(f125,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(f340,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption,[],[f193,f192,f191,f190,f202,f201,f200,f199,f198,f197,f196,f195,f194,f205,f204,f203,f208,f207,f206,f216,f215,f214,f213,f212,f211,f210,f209,f218,f217,f226,f225,f224,f223,f222,f221,f220,f219,f231,f230,f229,f228,f227,f233,f232,f235,f234,f237,f236,f240,f239,f238,f243,f242,f241,f248,f247,f246,f245,f244,f250,f249,f254,f253,f252,f251,f255,f257,f256,f258,f260,f259,f262,f261,f264,f263,f266,f268,f267,f270,f269,f277,f276,f275,f274,f273,f327,f328,f278,f281,f280,f279,f282,f283,f284,f285,f287,f338,f288,f330,f331,f332,f293,f292,f294,f295,f299,f298,f297,f296,f300,f333,f334,f335,f304,f305,f336,f307,f306,f337,f310,f309,f312,f313,f315,f314,f319,f318,f339,f317,f316]) ).
fof(f316,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& sz00 != X0 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(f317,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f339,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption,[],[f193,f192,f191,f190,f202,f201,f200,f199,f198,f197,f196,f195,f194,f205,f204,f203,f208,f207,f206,f216,f215,f214,f213,f212,f211,f210,f209,f218,f217,f226,f225,f224,f223,f222,f221,f220,f219,f231,f230,f229,f228,f227,f233,f232,f235,f234,f237,f236,f240,f239,f238,f243,f242,f241,f248,f247,f246,f245,f244,f250,f249,f254,f253,f252,f251,f255,f257,f256,f258,f260,f259,f262,f261,f264,f263,f266,f268,f267,f270,f269,f277,f276,f275,f274,f273,f327,f328,f278,f281,f280,f279,f282,f283,f284,f285,f287,f338,f288,f330,f331,f332,f293,f292,f294,f295,f299,f298,f297,f296,f300,f333,f334,f335,f304,f305,f336,f307,f306,f337,f310,f309,f312,f313,f315,f314,f319,f318]) ).
fof(f318,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f319,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f314,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f315,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f313,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f312,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f309,plain,
! [X0,X1] :
( aNaturalNumber0(sK19(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f189,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK19(X0,X1)) = X1
& aNaturalNumber0(sK19(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f187,f188]) ).
fof(f188,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK19(X0,X1)) = X1
& aNaturalNumber0(sK19(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f187,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f186]) ).
fof(f186,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f310,plain,
! [X0,X1] :
( sdtpldt0(X0,sK19(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f337,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f311]) ).
fof(f311,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f306,plain,
! [X0,X1] :
( aNaturalNumber0(sK18(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK18(X0,X1)) = X1
& aNaturalNumber0(sK18(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f183,f184]) ).
fof(f184,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK18(X0,X1)) = X1
& aNaturalNumber0(sK18(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f183,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f182]) ).
fof(f182,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f307,plain,
! [X0,X1] :
( sdtasdt0(X0,sK18(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f336,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f308]) ).
fof(f308,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f305,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f304,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sz00 != X1
& doDivides0(X0,X1) )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(f335,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f301]) ).
fof(f301,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f180]) ).
fof(f180,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f334,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f302]) ).
fof(f302,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f333,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f303]) ).
fof(f303,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f300,plain,
! [X2,X0,X1] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
fof(f296,plain,
! [X2,X0,X1] :
( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(f297,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f298,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f299,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f295,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(f294,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(f292,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtpldt0(X0,X1)
=> ( sz00 = X1
& sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f293,plain,
! [X0,X1] :
( sz00 = X1
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f332,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f289]) ).
fof(f289,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f178]) ).
fof(f178,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f331,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f290]) ).
fof(f290,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f330,plain,
! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f291]) ).
fof(f291,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f288,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 != X0
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(f338,plain,
! [X1] :
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f329]) ).
fof(f329,plain,
! [X1] :
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f286]) ).
fof(f286,plain,
! [X0,X1] :
( X0 != X1
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f285,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f284,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f279,plain,
! [X0] :
( aNaturalNumber0(sK17(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( isPrime0(sK17(X0))
& doDivides0(sK17(X0),X0)
& aNaturalNumber0(sK17(X0)) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f82,f176]) ).
fof(f176,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( isPrime0(sK17(X0))
& doDivides0(sK17(X0),X0)
& aNaturalNumber0(sK17(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
fof(f280,plain,
! [X0] :
( doDivides0(sK17(X0),X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f281,plain,
! [X0] :
( isPrime0(sK17(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f273,plain,
! [X2,X0] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f274,plain,
! [X0] :
( sP4(X0)
| aNaturalNumber0(sK16(X0))
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f275,plain,
! [X0] :
( sP4(X0)
| doDivides0(sK16(X0),X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f276,plain,
! [X0] :
( sP4(X0)
| sz10 != sK16(X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f277,plain,
! [X0] :
( sP4(X0)
| sK16(X0) != X0
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f267,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != X0
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(f268,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f266,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( sP3(X1,X2)
| sP2(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3)
| sP1(X2)
| sz10 = X2
| sz00 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1,X2] :
( sP3(X1,X2)
| sP2(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X3] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ( ~ isPrime0(X2)
& ( sP1(X2)
| sz10 = X2
| sz00 = X2 ) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f70,f138,f137,f136,f135]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X3] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ( ~ isPrime0(X2)
& ( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
| sz10 = X2
| sz00 = X2 ) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X3] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ( ~ isPrime0(X2)
& ( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
| sz10 = X2
| sz00 = X2 ) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( ( doDivides0(X2,sdtasdt0(X0,X1))
| ? [X3] :
( sdtasdt0(X0,X1) = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& ( isPrime0(X2)
| ( ! [X4] :
( ( doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
=> ( X2 = X4
| sz10 = X4 ) )
& sz10 != X2
& sz00 != X2 ) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( ( doDivides0(X2,sdtasdt0(X0,X1))
| ? [X3] :
( sdtasdt0(X0,X1) = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& ( isPrime0(X2)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( sdtasdt0(X3,X4) = X2
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X2 = X3
| sz10 = X3 ) )
& sz10 != X2
& sz00 != X2 ) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( doDivides0(X2,X1)
& ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) ) )
| ( doDivides0(X2,X0)
& ? [X3] :
( sdtasdt0(X2,X3) = X0
& aNaturalNumber0(X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
fof(f252,plain,
! [X2,X3,X0,X1] :
( sP3(X1,X2)
| sP2(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f253,plain,
! [X2,X0,X1] :
( sP3(X1,X2)
| sP2(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| sP1(X2)
| sz10 = X2
| sz00 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f254,plain,
! [X2,X0,X1] :
( sP3(X1,X2)
| sP2(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f232,plain,
sz00 != xk,
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( sz10 != xk
& sz00 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
~ ( sz10 = xk
| sz00 = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(f233,plain,
sz10 != xk,
inference(cnf_transformation,[],[f66]) ).
fof(f221,plain,
! [X2,X1] :
( xp = X1
| sz10 = X1
| sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f222,plain,
! [X1] :
( xp = X1
| sz10 = X1
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f200,plain,
! [X0,X1] :
( xr = X0
| sz10 = X0
| sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f201,plain,
! [X0] :
( xr = X0
| sz10 = X0
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM505+3 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 06:55:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (30632)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (30635)WARNING: value z3 for option sas not known
% 0.14/0.38 % (30633)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (30634)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (30636)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (30635)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (30637)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (30638)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (30639)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.39 Detected minimum model sizes of [3]
% 0.14/0.39 Detected maximum model sizes of [max]
% 0.14/0.39 TRYING [3]
% 0.21/0.40 % (30635)First to succeed.
% 0.21/0.40 % (30638)Also succeeded, but the first one will report.
% 0.21/0.40 % (30635)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30632"
% 0.21/0.40 % (30635)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41 % (30635)------------------------------
% 0.21/0.41 % (30635)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.41 % (30635)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (30635)Memory used [KB]: 1207
% 0.21/0.41 % (30635)Time elapsed: 0.025 s
% 0.21/0.41 % (30635)Instructions burned: 43 (million)
% 0.21/0.41 % (30632)Success in time 0.044 s
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