TSTP Solution File: NUM491+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM491+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Sun May 5 08:31:45 EDT 2024
% Result : Theorem 0.16s 0.41s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 88 ( 39 unt; 0 def)
% Number of atoms : 265 ( 99 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 269 ( 92 ~; 58 |; 93 &)
% ( 20 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 20 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 42 ( 25 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f397,plain,
$false,
inference(avatar_sat_refutation,[],[f305,f310,f315,f320,f325,f330,f335,f340,f345,f350,f355,f360,f365,f369,f375,f380,f385,f390,f395,f396]) ).
fof(f396,plain,
( ~ spl17_4
| ~ spl17_14 ),
inference(avatar_split_clause,[],[f370,f367,f317]) ).
fof(f317,plain,
( spl17_4
<=> aNaturalNumber0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f367,plain,
( spl17_14
<=> ! [X0] :
( sdtasdt0(xp,X0) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f370,plain,
( ~ aNaturalNumber0(xm)
| ~ spl17_14 ),
inference(equality_resolution,[],[f368]) ).
fof(f368,plain,
( ! [X0] :
( sdtasdt0(xp,X0) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(X0) )
| ~ spl17_14 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f395,plain,
spl17_19,
inference(avatar_split_clause,[],[f199,f392]) ).
fof(f392,plain,
( spl17_19
<=> sdtlseqdt0(xp,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f199,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( sdtlseqdt0(xp,xn)
& xn = sdtpldt0(xp,sK8)
& aNaturalNumber0(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f42,f135]) ).
fof(f135,plain,
( ? [X0] :
( xn = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( xn = sdtpldt0(xp,sK8)
& aNaturalNumber0(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
( sdtlseqdt0(xp,xn)
& ? [X0] :
( xn = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(f390,plain,
~ spl17_18,
inference(avatar_split_clause,[],[f188,f387]) ).
fof(f387,plain,
( spl17_18
<=> sz10 = xp ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f188,plain,
sz10 != xp,
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK7)
& aNaturalNumber0(sK7)
& 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,[sK7])],[f56,f133]) ).
fof(f133,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK7)
& aNaturalNumber0(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f56,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,[],[f55]) ).
fof(f55,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,[],[f50]) ).
fof(f50,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(f385,plain,
~ spl17_17,
inference(avatar_split_clause,[],[f187,f382]) ).
fof(f382,plain,
( spl17_17
<=> sz00 = xp ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f187,plain,
sz00 != xp,
inference(cnf_transformation,[],[f134]) ).
fof(f380,plain,
spl17_16,
inference(avatar_split_clause,[],[f186,f377]) ).
fof(f377,plain,
( spl17_16
<=> sdtlseqdt0(xr,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f186,plain,
sdtlseqdt0(xr,xn),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( sdtlseqdt0(xr,xn)
& xn = sdtpldt0(xr,sK6)
& aNaturalNumber0(sK6)
& xn != xr ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f44,f131]) ).
fof(f131,plain,
( ? [X0] :
( xn = sdtpldt0(xr,X0)
& aNaturalNumber0(X0) )
=> ( xn = sdtpldt0(xr,sK6)
& aNaturalNumber0(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f44,axiom,
( sdtlseqdt0(xr,xn)
& ? [X0] :
( xn = sdtpldt0(xr,X0)
& aNaturalNumber0(X0) )
& xn != xr ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1894) ).
fof(f375,plain,
~ spl17_15,
inference(avatar_split_clause,[],[f183,f372]) ).
fof(f372,plain,
( spl17_15
<=> xn = xr ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
fof(f183,plain,
xn != xr,
inference(cnf_transformation,[],[f132]) ).
fof(f369,plain,
spl17_14,
inference(avatar_split_clause,[],[f173,f367]) ).
fof(f173,plain,
! [X0] :
( sdtasdt0(xp,X0) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
( ~ doDivides0(xp,sdtasdt0(xp,xm))
& ! [X0] :
( sdtasdt0(xp,X0) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ? [X0] :
( sdtasdt0(xp,X0) = sdtasdt0(xp,xm)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
( doDivides0(xp,sdtasdt0(xp,xm))
| ? [X0] :
( sdtasdt0(xp,X0) = sdtasdt0(xp,xm)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f365,plain,
~ spl17_13,
inference(avatar_split_clause,[],[f290,f362]) ).
fof(f362,plain,
( spl17_13
<=> sP4(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
fof(f290,plain,
~ sP4(sz00),
inference(equality_resolution,[],[f233]) ).
fof(f233,plain,
! [X0] :
( sz00 != X0
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0] :
( ( sP4(X0)
| ( sK13(X0) != X0
& sz10 != sK13(X0)
& doDivides0(sK13(X0),X0)
& aNaturalNumber0(sK13(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,[sK13])],[f156,f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK13(X0) != X0
& sz10 != sK13(X0)
& doDivides0(sK13(X0),X0)
& aNaturalNumber0(sK13(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f156,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,[],[f155]) ).
fof(f155,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,[],[f154]) ).
fof(f154,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,[],[f128]) ).
fof(f128,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(f360,plain,
~ spl17_12,
inference(avatar_split_clause,[],[f289,f357]) ).
fof(f357,plain,
( spl17_12
<=> sP4(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f289,plain,
~ sP4(sz10),
inference(equality_resolution,[],[f234]) ).
fof(f234,plain,
! [X0] :
( sz10 != X0
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f355,plain,
spl17_11,
inference(avatar_split_clause,[],[f218,f352]) ).
fof(f352,plain,
( spl17_11
<=> aNaturalNumber0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f218,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f350,plain,
spl17_10,
inference(avatar_split_clause,[],[f217,f347]) ).
fof(f347,plain,
( spl17_10
<=> aNaturalNumber0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f217,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f345,plain,
spl17_9,
inference(avatar_split_clause,[],[f197,f342]) ).
fof(f342,plain,
( spl17_9
<=> aNaturalNumber0(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f197,plain,
aNaturalNumber0(sK8),
inference(cnf_transformation,[],[f136]) ).
fof(f340,plain,
spl17_8,
inference(avatar_split_clause,[],[f192,f337]) ).
fof(f337,plain,
( spl17_8
<=> aNaturalNumber0(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
fof(f192,plain,
aNaturalNumber0(sK7),
inference(cnf_transformation,[],[f134]) ).
fof(f335,plain,
spl17_7,
inference(avatar_split_clause,[],[f191,f332]) ).
fof(f332,plain,
( spl17_7
<=> isPrime0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f191,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f134]) ).
fof(f330,plain,
spl17_6,
inference(avatar_split_clause,[],[f184,f327]) ).
fof(f327,plain,
( spl17_6
<=> aNaturalNumber0(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f184,plain,
aNaturalNumber0(sK6),
inference(cnf_transformation,[],[f132]) ).
fof(f325,plain,
spl17_5,
inference(avatar_split_clause,[],[f182,f322]) ).
fof(f322,plain,
( spl17_5
<=> aNaturalNumber0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f182,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(f320,plain,
spl17_4,
inference(avatar_split_clause,[],[f181,f317]) ).
fof(f181,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f315,plain,
spl17_3,
inference(avatar_split_clause,[],[f180,f312]) ).
fof(f312,plain,
( spl17_3
<=> aNaturalNumber0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f180,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f310,plain,
spl17_2,
inference(avatar_split_clause,[],[f177,f307]) ).
fof(f307,plain,
( spl17_2
<=> aNaturalNumber0(xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f177,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
( xr = sdtmndt0(xn,xp)
& xn = sdtpldt0(xp,xr)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(f305,plain,
~ spl17_1,
inference(avatar_split_clause,[],[f174,f302]) ).
fof(f302,plain,
( spl17_1
<=> doDivides0(xp,sdtasdt0(xp,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f174,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.17 % Problem : NUM491+3 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.18 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.38 % Computer : n029.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8042.1875MB
% 0.11/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri May 3 14:59:08 EDT 2024
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % (22398)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.40 % (22402)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.40 % (22405)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)
% 0.11/0.40 % (22399)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.40 % (22404)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)
% 0.11/0.40 % (22403)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)
% 0.11/0.40 % (22401)WARNING: value z3 for option sas not known
% 0.16/0.40 % (22400)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.40 % (22401)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)
% 0.16/0.41 % (22404)Also succeeded, but the first one will report.
% 0.16/0.41 % (22403)First to succeed.
% 0.16/0.41 % (22403)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22398"
% 0.16/0.41 % (22403)Refutation found. Thanks to Tanya!
% 0.16/0.41 % SZS status Theorem for theBenchmark
% 0.16/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.41 % (22403)------------------------------
% 0.16/0.41 % (22403)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.41 % (22403)Termination reason: Refutation
% 0.16/0.41
% 0.16/0.41 % (22403)Memory used [KB]: 977
% 0.16/0.41 % (22403)Time elapsed: 0.007 s
% 0.16/0.41 % (22403)Instructions burned: 12 (million)
% 0.16/0.41 % (22398)Success in time 0.019 s
%------------------------------------------------------------------------------