TSTP Solution File: NUM460+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM460+2 : 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 : 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 : Sun May 5 08:28:29 EDT 2024
% Result : Theorem 2.37s 0.73s
% Output : Refutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 141 ( 45 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 148 ( 48 ~; 36 |; 56 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 38 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6266,plain,
$false,
inference(resolution,[],[f6265,f74]) ).
fof(f74,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( ~ sdtlseqdt0(xm,xl)
& ! [X0] :
( xl != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) )
& sdtlseqdt0(xn,xl)
& xl = sdtpldt0(xn,sK0)
& aNaturalNumber0(sK0)
& sdtlseqdt0(xm,xn)
& xn = sdtpldt0(xm,sK1)
& aNaturalNumber0(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f61,f63,f62]) ).
fof(f62,plain,
( ? [X1] :
( xl = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
=> ( xl = sdtpldt0(xn,sK0)
& aNaturalNumber0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
( ? [X2] :
( xn = sdtpldt0(xm,X2)
& aNaturalNumber0(X2) )
=> ( xn = sdtpldt0(xm,sK1)
& aNaturalNumber0(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
( ~ sdtlseqdt0(xm,xl)
& ! [X0] :
( xl != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) )
& sdtlseqdt0(xn,xl)
& ? [X1] :
( xl = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X2] :
( xn = sdtpldt0(xm,X2)
& aNaturalNumber0(X2) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
( ~ sdtlseqdt0(xm,xl)
& ! [X2] :
( xl != sdtpldt0(xm,X2)
| ~ aNaturalNumber0(X2) )
& sdtlseqdt0(xn,xl)
& ? [X0] :
( xl = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( xn = sdtpldt0(xm,X1)
& aNaturalNumber0(X1) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
( ~ sdtlseqdt0(xm,xl)
& ! [X2] :
( xl != sdtpldt0(xm,X2)
| ~ aNaturalNumber0(X2) )
& sdtlseqdt0(xn,xl)
& ? [X0] :
( xl = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( xn = sdtpldt0(xm,X1)
& aNaturalNumber0(X1) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
~ ( ( sdtlseqdt0(xn,xl)
& ? [X0] :
( xl = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( xn = sdtpldt0(xm,X1)
& aNaturalNumber0(X1) ) )
=> ( sdtlseqdt0(xm,xl)
| ? [X2] :
( xl = sdtpldt0(xm,X2)
& aNaturalNumber0(X2) ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xl)
& ? [X0] :
( xl = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( xn = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) ) )
=> ( sdtlseqdt0(xm,xl)
| ? [X0] :
( xl = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) ) ) ),
inference(negated_conjecture,[],[f23]) ).
fof(f23,conjecture,
( ( sdtlseqdt0(xn,xl)
& ? [X0] :
( xl = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( xn = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) ) )
=> ( sdtlseqdt0(xm,xl)
| ? [X0] :
( xl = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f6265,plain,
~ aNaturalNumber0(sK0),
inference(resolution,[],[f6264,f71]) ).
fof(f71,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f64]) ).
fof(f6264,plain,
( ~ aNaturalNumber0(sK1)
| ~ aNaturalNumber0(sK0) ),
inference(resolution,[],[f6263,f95]) ).
fof(f95,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f37]) ).
fof(f37,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/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6263,plain,
~ aNaturalNumber0(sdtpldt0(sK0,sK1)),
inference(trivial_inequality_removal,[],[f6254]) ).
fof(f6254,plain,
( xl != xl
| ~ aNaturalNumber0(sdtpldt0(sK0,sK1)) ),
inference(superposition,[],[f77,f6002]) ).
fof(f6002,plain,
xl = sdtpldt0(xm,sdtpldt0(sK0,sK1)),
inference(forward_demodulation,[],[f6001,f75]) ).
fof(f75,plain,
xl = sdtpldt0(xn,sK0),
inference(cnf_transformation,[],[f64]) ).
fof(f6001,plain,
sdtpldt0(xn,sK0) = sdtpldt0(xm,sdtpldt0(sK0,sK1)),
inference(forward_demodulation,[],[f5987,f303]) ).
fof(f303,plain,
sdtpldt0(sK1,sK0) = sdtpldt0(sK0,sK1),
inference(resolution,[],[f253,f71]) ).
fof(f253,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sK0) = sdtpldt0(sK0,X0) ),
inference(resolution,[],[f97,f74]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f41]) ).
fof(f41,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/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f5987,plain,
sdtpldt0(xn,sK0) = sdtpldt0(xm,sdtpldt0(sK1,sK0)),
inference(resolution,[],[f3006,f74]) ).
fof(f3006,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK1,X0)) ),
inference(forward_demodulation,[],[f2982,f72]) ).
fof(f72,plain,
xn = sdtpldt0(xm,sK1),
inference(cnf_transformation,[],[f64]) ).
fof(f2982,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xm,sK1),X0) = sdtpldt0(xm,sdtpldt0(sK1,X0)) ),
inference(resolution,[],[f1077,f79]) ).
fof(f79,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773) ).
fof(f1077,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X1,sK1),X0) = sdtpldt0(X1,sdtpldt0(sK1,X0)) ),
inference(resolution,[],[f109,f71]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f77,plain,
! [X0] :
( xl != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM460+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35 % Computer : n019.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri May 3 15:11:38 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % (18222)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.37 % (18227)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)
% 0.12/0.37 % (18225)WARNING: value z3 for option sas not known
% 0.12/0.37 % (18226)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37 % (18229)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)
% 0.12/0.37 % (18224)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.37 % (18225)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)
% 0.12/0.37 % (18228)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)
% 0.12/0.37 TRYING [1]
% 0.12/0.37 % (18223)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37 TRYING [2]
% 0.12/0.37 TRYING [3]
% 0.12/0.37 TRYING [1]
% 0.12/0.37 TRYING [2]
% 0.12/0.38 TRYING [3]
% 0.19/0.38 TRYING [4]
% 0.19/0.38 TRYING [4]
% 0.19/0.43 TRYING [5]
% 0.19/0.43 TRYING [5]
% 1.36/0.54 TRYING [6]
% 1.36/0.55 TRYING [6]
% 1.51/0.60 TRYING [1]
% 1.51/0.60 TRYING [2]
% 1.51/0.60 TRYING [3]
% 1.51/0.61 TRYING [4]
% 2.08/0.65 TRYING [5]
% 2.37/0.73 % (18228)First to succeed.
% 2.37/0.73 % (18228)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18222"
% 2.37/0.73 % (18228)Refutation found. Thanks to Tanya!
% 2.37/0.73 % SZS status Theorem for theBenchmark
% 2.37/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.37/0.73 % (18228)------------------------------
% 2.37/0.73 % (18228)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.37/0.73 % (18228)Termination reason: Refutation
% 2.37/0.73
% 2.37/0.73 % (18228)Memory used [KB]: 5088
% 2.37/0.73 % (18228)Time elapsed: 0.360 s
% 2.37/0.73 % (18228)Instructions burned: 716 (million)
% 2.37/0.73 % (18222)Success in time 0.365 s
%------------------------------------------------------------------------------