%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM491+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:25 PM UTC 2026
% Result : Theorem 2.66s 1.28s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 76 ( 10 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 93 ( 40 ~; 35 |; 13 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 30 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f48,conjecture,
doDivides0(xp,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f50,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(flattening,[],[f49]) ).
fof(f74,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f75,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f74]) ).
fof(f84,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f85,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f84]) ).
fof(f115,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f85]) ).
fof(f116,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK0(X0,X1))
& sdtasdt0(X0,sK0(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f116]) ).
fof(f128,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f129,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f141,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f50]) ).
fof(f156,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f163,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f206,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f163]) ).
fof(f402,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f206,f156]) ).
fof(f403,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f402,f141]) ).
fof(f420,plain,
~ aNaturalNumber0(xp),
inference(forward_subsumption_resolution,[],[f403,f129]) ).
fof(f421,plain,
$false,
inference(forward_subsumption_resolution,[],[f420,f128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM491+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:10:30 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.66/1.27 % (2727451)Detected formulas, will run a generic FOF schedule.
% 2.66/1.27 % (2727460)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1955804476:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.27 % (2727460)First to succeed.
% 2.66/1.27 % (2727460)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2727451"
% 2.66/1.27 % (2727457)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3589360157:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.27 % (2727462)dis-21_1_sil=8000:lcm=predicate:random_seed=2428116802:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.66/1.27 % (2727459)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3794265259:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.27 % (2727458)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=780959128:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.28 % (2727456)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3592042446:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.28 % (2727461)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=529551772:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.28 % (2727459)Also succeeded, but the first one will report.
% 2.66/1.28 % (2727462)Also succeeded, but the first one will report.
% 2.66/1.28 % (2727461)Also succeeded, but the first one will report.
% 2.66/1.28 % (2727460)Refutation found. Thanks to Tanya!
% 2.66/1.28 % SZS status Theorem for theBenchmark
% 2.66/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.28 % (2727460)------------------------------
% 2.66/1.28 % (2727460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.28 % (2727460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.28 % (2727460)CaDiCaL version: 2.1.3
% 2.66/1.28 % (2727460)Termination reason: Refutation
% 2.66/1.28 % (2727460)Time elapsed: 0.004 s
% 2.66/1.28 % (2727460)Peak memory usage: 88 MB
% 2.66/1.28 % (2727460)Instructions burned: 9 (million)
% 2.66/1.28 % (2727460)------------------------------
% 2.66/1.28 % (2727460)------------------------------
% 2.66/1.28 % (2727451)Success in time 0.311 s
% 2.66/1.28 % Vampire exiting
%------------------------------------------------------------------------------