TSTP Solution File: RNG046+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG046+1 : 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 : n009.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 02:40:44 EDT 2024
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 32
% Syntax : Number of formulae : 186 ( 25 unt; 0 def)
% Number of atoms : 467 ( 123 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 477 ( 196 ~; 200 |; 54 &)
% ( 19 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 20 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 73 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5673,plain,
$false,
inference(avatar_sat_refutation,[],[f88,f196,f199,f211,f281,f298,f301,f307,f318,f397,f401,f468,f477,f478,f479,f480,f481,f493,f497,f611,f872,f876,f4021,f4024,f4056,f5670]) ).
fof(f5670,plain,
( ~ spl2_13
| ~ spl2_15 ),
inference(avatar_contradiction_clause,[],[f5669]) ).
fof(f5669,plain,
( $false
| ~ spl2_13
| ~ spl2_15 ),
inference(subsumption_resolution,[],[f5668,f50]) ).
fof(f50,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(flattening,[],[f20]) ).
fof(f20,negated_conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f5668,plain,
( sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy)
| ~ spl2_13
| ~ spl2_15 ),
inference(forward_demodulation,[],[f5667,f989]) ).
fof(f989,plain,
( sdtasdt0(xx,xy) = smndt0(sdtasdt0(xx,smndt0(xy)))
| ~ spl2_13
| ~ spl2_15 ),
inference(forward_demodulation,[],[f982,f642]) ).
fof(f642,plain,
( sdtasdt0(xx,xy) = sdtasdt0(xy,xx)
| ~ spl2_15 ),
inference(resolution,[],[f631,f52]) ).
fof(f52,plain,
aScalar0(xy),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
( aScalar0(xy)
& aScalar0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f631,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,xx) = sdtasdt0(xx,X0) )
| ~ spl2_15 ),
inference(resolution,[],[f610,f51]) ).
fof(f51,plain,
aScalar0(xx),
inference(cnf_transformation,[],[f18]) ).
fof(f610,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f609,plain,
( spl2_15
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f982,plain,
( sdtasdt0(xy,xx) = smndt0(sdtasdt0(xx,smndt0(xy)))
| ~ spl2_13
| ~ spl2_15 ),
inference(superposition,[],[f521,f808]) ).
fof(f808,plain,
( sdtasdt0(xy,smndt0(xx)) = sdtasdt0(xx,smndt0(xy))
| ~ spl2_15 ),
inference(superposition,[],[f803,f644]) ).
fof(f644,plain,
( sdtasdt0(xy,smndt0(xx)) = smndt0(sdtasdt0(xx,xy))
| ~ spl2_15 ),
inference(superposition,[],[f384,f642]) ).
fof(f384,plain,
sdtasdt0(xy,smndt0(xx)) = smndt0(sdtasdt0(xy,xx)),
inference(resolution,[],[f286,f52]) ).
fof(f286,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,smndt0(xx)) = smndt0(sdtasdt0(X0,xx)) ),
inference(resolution,[],[f72,f51]) ).
fof(f72,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).
fof(f803,plain,
smndt0(sdtasdt0(xx,xy)) = sdtasdt0(xx,smndt0(xy)),
inference(resolution,[],[f287,f51]) ).
fof(f287,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,smndt0(xy)) = smndt0(sdtasdt0(X0,xy)) ),
inference(resolution,[],[f72,f52]) ).
fof(f521,plain,
( sdtasdt0(xy,xx) = smndt0(sdtasdt0(xy,smndt0(xx)))
| ~ spl2_13 ),
inference(forward_demodulation,[],[f504,f384]) ).
fof(f504,plain,
( sdtasdt0(xy,xx) = smndt0(smndt0(sdtasdt0(xy,xx)))
| ~ spl2_13 ),
inference(resolution,[],[f487,f94]) ).
fof(f94,plain,
! [X0] :
( ~ aScalar0(X0)
| smndt0(smndt0(X0)) = X0 ),
inference(resolution,[],[f64,f66]) ).
fof(f66,plain,
! [X0] :
( sP0(X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( sP0(X0)
| ~ aScalar0(X0) ),
inference(definition_folding,[],[f28,f45]) ).
fof(f45,plain,
! [X0] :
( ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f28,plain,
! [X0] :
( ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 )
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( aScalar0(X0)
=> ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).
fof(f64,plain,
! [X0] :
( ~ sP0(X0)
| smndt0(smndt0(X0)) = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f487,plain,
( aScalar0(sdtasdt0(xy,xx))
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f486,plain,
( spl2_13
<=> aScalar0(sdtasdt0(xy,xx)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f5667,plain,
( sdtasdt0(smndt0(xx),smndt0(xy)) = smndt0(sdtasdt0(xx,smndt0(xy)))
| ~ spl2_15 ),
inference(forward_demodulation,[],[f5647,f1071]) ).
fof(f1071,plain,
( sdtasdt0(xx,smndt0(xy)) = sdtasdt0(smndt0(xx),xy)
| ~ spl2_15 ),
inference(forward_demodulation,[],[f1070,f808]) ).
fof(f1070,plain,
( sdtasdt0(xy,smndt0(xx)) = sdtasdt0(smndt0(xx),xy)
| ~ spl2_15 ),
inference(forward_demodulation,[],[f1053,f644]) ).
fof(f1053,plain,
smndt0(sdtasdt0(xx,xy)) = sdtasdt0(smndt0(xx),xy),
inference(resolution,[],[f346,f51]) ).
fof(f346,plain,
! [X0] :
( ~ aScalar0(X0)
| smndt0(sdtasdt0(X0,xy)) = sdtasdt0(smndt0(X0),xy) ),
inference(resolution,[],[f73,f52]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f5647,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) = smndt0(sdtasdt0(smndt0(xx),xy)),
inference(resolution,[],[f802,f51]) ).
fof(f802,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(smndt0(X0),smndt0(xy)) = smndt0(sdtasdt0(smndt0(X0),xy)) ),
inference(resolution,[],[f287,f57]) ).
fof(f57,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
fof(f4056,plain,
( ~ spl2_8
| spl2_18
| ~ spl2_19 ),
inference(avatar_contradiction_clause,[],[f4055]) ).
fof(f4055,plain,
( $false
| ~ spl2_8
| spl2_18
| ~ spl2_19 ),
inference(subsumption_resolution,[],[f4054,f297]) ).
fof(f297,plain,
( aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00)))
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f295,plain,
( spl2_8
<=> aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f4054,plain,
( ~ aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00)))
| spl2_18
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f4052]) ).
fof(f4052,plain,
( sz00 != sz00
| ~ aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00)))
| spl2_18
| ~ spl2_19 ),
inference(superposition,[],[f56,f4046]) ).
fof(f4046,plain,
( sz00 = szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00)))
| spl2_18
| ~ spl2_19 ),
inference(subsumption_resolution,[],[f4045,f4020]) ).
fof(f4020,plain,
( aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00))))
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f4018]) ).
fof(f4018,plain,
( spl2_19
<=> aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f4045,plain,
( sz00 = szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00)))
| ~ aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00))))
| spl2_18 ),
inference(resolution,[],[f4016,f67]) ).
fof(f67,plain,
! [X0] :
( aNaturalNumber0(sK1(X0))
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ( szszuzczcdt0(sK1(X0)) = X0
& aNaturalNumber0(sK1(X0)) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f30,f48]) ).
fof(f48,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aNaturalNumber0(X1) )
=> ( szszuzczcdt0(sK1(X0)) = X0
& aNaturalNumber0(sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( sz00 != X0
& aNaturalNumber0(X0) )
=> ? [X1] :
( szszuzczcdt0(X1) = X0
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).
fof(f4016,plain,
( ~ aNaturalNumber0(sK1(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00)))))
| spl2_18 ),
inference(avatar_component_clause,[],[f4014]) ).
fof(f4014,plain,
( spl2_18
<=> aNaturalNumber0(sK1(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f56,plain,
! [X0] :
( sz00 != szszuzczcdt0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( sz00 != szszuzczcdt0(X0)
& aNaturalNumber0(szszuzczcdt0(X0)) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != szszuzczcdt0(X0)
& aNaturalNumber0(szszuzczcdt0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
fof(f4024,plain,
( ~ spl2_8
| spl2_19 ),
inference(avatar_contradiction_clause,[],[f4023]) ).
fof(f4023,plain,
( $false
| ~ spl2_8
| spl2_19 ),
inference(subsumption_resolution,[],[f4022,f297]) ).
fof(f4022,plain,
( ~ aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00)))
| spl2_19 ),
inference(resolution,[],[f4019,f55]) ).
fof(f55,plain,
! [X0] :
( aNaturalNumber0(szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f4019,plain,
( ~ aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00))))
| spl2_19 ),
inference(avatar_component_clause,[],[f4018]) ).
fof(f4021,plain,
( ~ spl2_18
| spl2_19
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f3196,f193,f4018,f4014]) ).
fof(f193,plain,
( spl2_4
<=> aNaturalNumber0(szszuzczcdt0(sz00)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f3196,plain,
( aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00))))
| ~ aNaturalNumber0(sK1(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00)))))
| ~ spl2_4 ),
inference(superposition,[],[f55,f2537]) ).
fof(f2537,plain,
( szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00))) = szszuzczcdt0(sK1(szszuzczcdt0(szszuzczcdt0(szszuzczcdt0(sz00)))))
| ~ spl2_4 ),
inference(resolution,[],[f183,f195]) ).
fof(f195,plain,
( aNaturalNumber0(szszuzczcdt0(sz00))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f183,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| szszuzczcdt0(szszuzczcdt0(X0)) = szszuzczcdt0(sK1(szszuzczcdt0(szszuzczcdt0(X0)))) ),
inference(resolution,[],[f180,f55]) ).
fof(f180,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) = szszuzczcdt0(sK1(szszuzczcdt0(X0))) ),
inference(subsumption_resolution,[],[f178,f56]) ).
fof(f178,plain,
! [X0] :
( sz00 = szszuzczcdt0(X0)
| szszuzczcdt0(X0) = szszuzczcdt0(sK1(szszuzczcdt0(X0)))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f68,f55]) ).
fof(f68,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| szszuzczcdt0(sK1(X0)) = X0 ),
inference(cnf_transformation,[],[f49]) ).
fof(f876,plain,
spl2_16,
inference(avatar_contradiction_clause,[],[f875]) ).
fof(f875,plain,
( $false
| spl2_16 ),
inference(subsumption_resolution,[],[f874,f52]) ).
fof(f874,plain,
( ~ aScalar0(xy)
| spl2_16 ),
inference(duplicate_literal_removal,[],[f873]) ).
fof(f873,plain,
( ~ aScalar0(xy)
| ~ aScalar0(xy)
| spl2_16 ),
inference(resolution,[],[f867,f71]) ).
fof(f71,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(f867,plain,
( ~ aScalar0(sdtasdt0(xy,xy))
| spl2_16 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f865,plain,
( spl2_16
<=> aScalar0(sdtasdt0(xy,xy)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f872,plain,
( ~ spl2_16
| spl2_17 ),
inference(avatar_split_clause,[],[f863,f869,f865]) ).
fof(f869,plain,
( spl2_17
<=> aScalar0(sdtasdt0(xy,smndt0(xy))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f863,plain,
( aScalar0(sdtasdt0(xy,smndt0(xy)))
| ~ aScalar0(sdtasdt0(xy,xy)) ),
inference(superposition,[],[f57,f804]) ).
fof(f804,plain,
sdtasdt0(xy,smndt0(xy)) = smndt0(sdtasdt0(xy,xy)),
inference(resolution,[],[f287,f52]) ).
fof(f611,plain,
( spl2_11
| spl2_15 ),
inference(avatar_split_clause,[],[f77,f609,f463]) ).
fof(f463,plain,
( spl2_11
<=> ! [X2] : ~ aScalar0(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f77,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
fof(f497,plain,
spl2_13,
inference(avatar_contradiction_clause,[],[f496]) ).
fof(f496,plain,
( $false
| spl2_13 ),
inference(subsumption_resolution,[],[f495,f52]) ).
fof(f495,plain,
( ~ aScalar0(xy)
| spl2_13 ),
inference(subsumption_resolution,[],[f494,f51]) ).
fof(f494,plain,
( ~ aScalar0(xx)
| ~ aScalar0(xy)
| spl2_13 ),
inference(resolution,[],[f488,f71]) ).
fof(f488,plain,
( ~ aScalar0(sdtasdt0(xy,xx))
| spl2_13 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f493,plain,
( ~ spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f388,f490,f486]) ).
fof(f490,plain,
( spl2_14
<=> aScalar0(sdtasdt0(xy,smndt0(xx))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f388,plain,
( aScalar0(sdtasdt0(xy,smndt0(xx)))
| ~ aScalar0(sdtasdt0(xy,xx)) ),
inference(superposition,[],[f57,f384]) ).
fof(f481,plain,
~ spl2_11,
inference(avatar_contradiction_clause,[],[f469]) ).
fof(f469,plain,
( $false
| ~ spl2_11 ),
inference(resolution,[],[f464,f54]) ).
fof(f54,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f464,plain,
( ! [X2] : ~ aScalar0(X2)
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f480,plain,
( ~ spl2_9
| ~ spl2_11 ),
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f472,plain,
( $false
| ~ spl2_9
| ~ spl2_11 ),
inference(resolution,[],[f464,f391]) ).
fof(f391,plain,
( aScalar0(sdtasdt0(xx,xx))
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f390,plain,
( spl2_9
<=> aScalar0(sdtasdt0(xx,xx)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f479,plain,
( ~ spl2_10
| ~ spl2_11 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f473,plain,
( $false
| ~ spl2_10
| ~ spl2_11 ),
inference(resolution,[],[f464,f396]) ).
fof(f396,plain,
( aScalar0(sdtasdt0(xx,smndt0(xx)))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f394,plain,
( spl2_10
<=> aScalar0(sdtasdt0(xx,smndt0(xx))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f478,plain,
~ spl2_11,
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f475,plain,
( $false
| ~ spl2_11 ),
inference(resolution,[],[f464,f51]) ).
fof(f477,plain,
~ spl2_11,
inference(avatar_contradiction_clause,[],[f476]) ).
fof(f476,plain,
( $false
| ~ spl2_11 ),
inference(resolution,[],[f464,f52]) ).
fof(f468,plain,
( spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f75,f466,f463]) ).
fof(f466,plain,
( spl2_12
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f75,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f401,plain,
spl2_9,
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f400,plain,
( $false
| spl2_9 ),
inference(subsumption_resolution,[],[f399,f51]) ).
fof(f399,plain,
( ~ aScalar0(xx)
| spl2_9 ),
inference(duplicate_literal_removal,[],[f398]) ).
fof(f398,plain,
( ~ aScalar0(xx)
| ~ aScalar0(xx)
| spl2_9 ),
inference(resolution,[],[f392,f71]) ).
fof(f392,plain,
( ~ aScalar0(sdtasdt0(xx,xx))
| spl2_9 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f397,plain,
( ~ spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f387,f394,f390]) ).
fof(f387,plain,
( aScalar0(sdtasdt0(xx,smndt0(xx)))
| ~ aScalar0(sdtasdt0(xx,xx)) ),
inference(superposition,[],[f57,f383]) ).
fof(f383,plain,
sdtasdt0(xx,smndt0(xx)) = smndt0(sdtasdt0(xx,xx)),
inference(resolution,[],[f286,f51]) ).
fof(f318,plain,
( ~ spl2_4
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f317,plain,
( $false
| ~ spl2_4
| ~ spl2_6 ),
inference(subsumption_resolution,[],[f316,f195]) ).
fof(f316,plain,
( ~ aNaturalNumber0(szszuzczcdt0(sz00))
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f314]) ).
fof(f314,plain,
( sz00 != sz00
| ~ aNaturalNumber0(szszuzczcdt0(sz00))
| ~ spl2_6 ),
inference(superposition,[],[f56,f279]) ).
fof(f279,plain,
( sz00 = szszuzczcdt0(szszuzczcdt0(sz00))
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f278,plain,
( spl2_6
<=> sz00 = szszuzczcdt0(szszuzczcdt0(sz00)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f307,plain,
( spl2_6
| spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f306]) ).
fof(f306,plain,
( $false
| spl2_6
| spl2_7
| ~ spl2_8 ),
inference(subsumption_resolution,[],[f305,f297]) ).
fof(f305,plain,
( ~ aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00)))
| spl2_6
| spl2_7 ),
inference(subsumption_resolution,[],[f304,f280]) ).
fof(f280,plain,
( sz00 != szszuzczcdt0(szszuzczcdt0(sz00))
| spl2_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f304,plain,
( sz00 = szszuzczcdt0(szszuzczcdt0(sz00))
| ~ aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00)))
| spl2_7 ),
inference(resolution,[],[f293,f67]) ).
fof(f293,plain,
( ~ aNaturalNumber0(sK1(szszuzczcdt0(szszuzczcdt0(sz00))))
| spl2_7 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f291,plain,
( spl2_7
<=> aNaturalNumber0(sK1(szszuzczcdt0(szszuzczcdt0(sz00)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f301,plain,
( ~ spl2_4
| spl2_8 ),
inference(avatar_contradiction_clause,[],[f300]) ).
fof(f300,plain,
( $false
| ~ spl2_4
| spl2_8 ),
inference(subsumption_resolution,[],[f299,f195]) ).
fof(f299,plain,
( ~ aNaturalNumber0(szszuzczcdt0(sz00))
| spl2_8 ),
inference(resolution,[],[f296,f55]) ).
fof(f296,plain,
( ~ aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00)))
| spl2_8 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f298,plain,
( ~ spl2_7
| spl2_8
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f271,f193,f295,f291]) ).
fof(f271,plain,
( aNaturalNumber0(szszuzczcdt0(szszuzczcdt0(sz00)))
| ~ aNaturalNumber0(sK1(szszuzczcdt0(szszuzczcdt0(sz00))))
| ~ spl2_4 ),
inference(superposition,[],[f55,f200]) ).
fof(f200,plain,
( szszuzczcdt0(szszuzczcdt0(sz00)) = szszuzczcdt0(sK1(szszuzczcdt0(szszuzczcdt0(sz00))))
| ~ spl2_4 ),
inference(resolution,[],[f195,f180]) ).
fof(f281,plain,
( ~ spl2_5
| ~ spl2_6
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f272,f193,f278,f274]) ).
fof(f274,plain,
( spl2_5
<=> aNaturalNumber0(sK1(sz00)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f272,plain,
( sz00 != szszuzczcdt0(szszuzczcdt0(sz00))
| ~ aNaturalNumber0(sK1(sz00))
| ~ spl2_4 ),
inference(inner_rewriting,[],[f270]) ).
fof(f270,plain,
( sz00 != szszuzczcdt0(szszuzczcdt0(sz00))
| ~ aNaturalNumber0(sK1(szszuzczcdt0(szszuzczcdt0(sz00))))
| ~ spl2_4 ),
inference(superposition,[],[f56,f200]) ).
fof(f211,plain,
( spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f210]) ).
fof(f210,plain,
( $false
| spl2_3
| ~ spl2_4 ),
inference(subsumption_resolution,[],[f209,f53]) ).
fof(f53,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
fof(f209,plain,
( ~ aNaturalNumber0(sz00)
| spl2_3
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f207]) ).
fof(f207,plain,
( sz00 != sz00
| ~ aNaturalNumber0(sz00)
| spl2_3
| ~ spl2_4 ),
inference(superposition,[],[f56,f203]) ).
fof(f203,plain,
( sz00 = szszuzczcdt0(sz00)
| spl2_3
| ~ spl2_4 ),
inference(subsumption_resolution,[],[f202,f195]) ).
fof(f202,plain,
( sz00 = szszuzczcdt0(sz00)
| ~ aNaturalNumber0(szszuzczcdt0(sz00))
| spl2_3 ),
inference(resolution,[],[f191,f67]) ).
fof(f191,plain,
( ~ aNaturalNumber0(sK1(szszuzczcdt0(sz00)))
| spl2_3 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f189,plain,
( spl2_3
<=> aNaturalNumber0(sK1(szszuzczcdt0(sz00))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f199,plain,
spl2_4,
inference(avatar_contradiction_clause,[],[f198]) ).
fof(f198,plain,
( $false
| spl2_4 ),
inference(subsumption_resolution,[],[f197,f53]) ).
fof(f197,plain,
( ~ aNaturalNumber0(sz00)
| spl2_4 ),
inference(resolution,[],[f194,f55]) ).
fof(f194,plain,
( ~ aNaturalNumber0(szszuzczcdt0(sz00))
| spl2_4 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f186,f193,f189]) ).
fof(f186,plain,
( aNaturalNumber0(szszuzczcdt0(sz00))
| ~ aNaturalNumber0(sK1(szszuzczcdt0(sz00))) ),
inference(superposition,[],[f55,f182]) ).
fof(f182,plain,
szszuzczcdt0(sz00) = szszuzczcdt0(sK1(szszuzczcdt0(sz00))),
inference(resolution,[],[f180,f53]) ).
fof(f88,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f65,f85,f82]) ).
fof(f82,plain,
( spl2_1
<=> ! [X0] : ~ sP0(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f85,plain,
( spl2_2
<=> sz0z00 = smndt0(sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f65,plain,
! [X0] :
( sz0z00 = smndt0(sz0z00)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG046+1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat May 18 12:22:08 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % (12582)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (12585)WARNING: value z3 for option sas not known
% 0.14/0.36 % (12585)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)
% 0.14/0.36 % (12589)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)
% 0.14/0.36 % (12586)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 % (12588)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)
% 0.14/0.36 % (12587)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)
% 0.14/0.36 % (12583)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (12584)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36 TRYING [1]
% 0.14/0.36 TRYING [1]
% 0.14/0.36 TRYING [2]
% 0.14/0.36 TRYING [2]
% 0.14/0.37 TRYING [3]
% 0.14/0.37 TRYING [3]
% 0.14/0.38 TRYING [4]
% 0.14/0.40 TRYING [4]
% 0.20/0.44 TRYING [5]
% 0.20/0.49 TRYING [5]
% 0.20/0.50 TRYING [1]
% 0.20/0.50 TRYING [2]
% 0.20/0.50 TRYING [3]
% 0.20/0.51 TRYING [4]
% 0.20/0.54 % (12585)First to succeed.
% 0.20/0.54 % (12585)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12582"
% 0.20/0.54 % (12585)Refutation found. Thanks to Tanya!
% 0.20/0.54 % SZS status Theorem for theBenchmark
% 0.20/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54 % (12585)------------------------------
% 0.20/0.54 % (12585)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.54 % (12585)Termination reason: Refutation
% 0.20/0.54
% 0.20/0.54 % (12585)Memory used [KB]: 2799
% 0.20/0.54 % (12585)Time elapsed: 0.183 s
% 0.20/0.54 % (12585)Instructions burned: 532 (million)
% 0.20/0.54 % (12582)Success in time 0.186 s
%------------------------------------------------------------------------------