%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM467+2 : 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 : n006.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 12:15:19 PM UTC 2026
% Result : Theorem 3.48s 1.38s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 10 unt; 1 def)
% Number of atoms : 89 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 37 ~; 30 |; 26 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 29 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f33,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(f34,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xl,X0) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
fof(f35,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f36,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
& doDivides0(xl,xn) ),
inference(rectify,[],[f34]) ).
fof(f39,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,X0) != sdtpldt0(xm,xn) )
& ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(ennf_transformation,[],[f36]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f58]) ).
fof(f65,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f66,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
( aNaturalNumber0(sK0)
& xm = sdtasdt0(xl,sK0)
& doDivides0(xl,xm)
& aNaturalNumber0(sK1)
& xn = sdtasdt0(xl,sK1)
& doDivides0(xl,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f37]) ).
fof(f76,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f33]) ).
fof(f78,plain,
xn = sdtasdt0(xl,sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f79,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f81,plain,
xm = sdtasdt0(xl,sK0),
inference(cnf_transformation,[],[f67]) ).
fof(f82,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f67]) ).
fof(f84,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,X0) != sdtpldt0(xm,xn) ),
inference(cnf_transformation,[],[f39]) ).
fof(f104,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f109,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f110,definition,
~ sP4(sdtpldt0(xm,xn)),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f111,plain,
! [X0] :
( sP4(sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0) ),
inference(inequality_splitting,[],[f84,f110]) ).
fof(f123,plain,
! [X0,X1] :
( sP4(sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X1)))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(superposition,[],[f111,f104]) ).
fof(f126,plain,
! [X0,X1] :
( sP4(sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X1)))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f123,f76]) ).
fof(f130,plain,
! [X0,X1] :
( sP4(sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X1)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f126,f109]) ).
fof(f211,plain,
~ sP4(sdtpldt0(xm,sdtasdt0(xl,sK1))),
inference(superposition,[],[f110,f78]) ).
fof(f212,plain,
~ sP4(sdtpldt0(sdtasdt0(xl,sK0),sdtasdt0(xl,sK1))),
inference(forward_demodulation,[],[f211,f81]) ).
fof(f267,plain,
( ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(sK1) ),
inference(resolution,[],[f130,f212]) ).
fof(f290,plain,
~ aNaturalNumber0(sK1),
inference(forward_subsumption_resolution,[],[f267,f82]) ).
fof(f293,plain,
$false,
inference(forward_subsumption_resolution,[],[f290,f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM467+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:02:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.48/1.38 % (3280522)Detected formulas, will run a generic FOF schedule.
% 3.48/1.38 % (3280528)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=2554515807:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.38 % (3280529)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=1116002891:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.38 % (3280531)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1669871300:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.38 % (3280530)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=769316936:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.38 % (3280527)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=2785193605:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.38 % (3280532)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4274756442:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.38 % (3280533)dis-21_1_sil=8000:lcm=predicate:random_seed=3837441216: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)
% 3.48/1.38 % (3280530)First to succeed.
% 3.48/1.38 % (3280530)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3280522"
% 3.48/1.38 % (3280531)Also succeeded, but the first one will report.
% 3.48/1.38 % (3280533)Instruction limit reached!
% 3.48/1.38 % (3280533)------------------------------
% 3.48/1.38 % (3280533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.38 % (3280533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.38 % (3280533)CaDiCaL version: 2.1.3
% 3.48/1.38 % (3280533)Termination reason: Instruction limit
% 3.48/1.38 % (3280533)Termination phase: Saturation
% 3.48/1.38 % (3280533)Time elapsed: 0.078 s
% 3.48/1.38 % (3280533)Peak memory usage: 90 MB
% 3.48/1.38 % (3280533)Instructions burned: 129 (million)
% 3.48/1.38 % (3280532)Instruction limit reached!
% 3.48/1.38 % (3280532)------------------------------
% 3.48/1.38 % (3280532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.38 % (3280532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.38 % (3280532)CaDiCaL version: 2.1.3
% 3.48/1.38 % (3280532)Termination reason: Instruction limit
% 3.48/1.38 % (3280532)Termination phase: Saturation
% 3.48/1.38 % (3280532)Time elapsed: 0.088 s
% 3.48/1.38 % (3280532)Peak memory usage: 90 MB
% 3.48/1.38 % (3280532)Instructions burned: 139 (million)
% 3.48/1.38 % (3280541)lrs+10_1_sil=8000:sp=occurrence:random_seed=3242820948:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.48/1.38 % (3280542)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4174713521:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.48/1.38 % (3280530)Refutation found. Thanks to Tanya!
% 3.48/1.38 % SZS status Theorem for theBenchmark
% 3.48/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.38 % (3280530)------------------------------
% 3.48/1.38 % (3280530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.38 % (3280530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.38 % (3280530)CaDiCaL version: 2.1.3
% 3.48/1.38 % (3280530)Termination reason: Refutation
% 3.48/1.38 % (3280530)Time elapsed: 0.006 s
% 3.48/1.38 % (3280530)Peak memory usage: 89 MB
% 3.48/1.38 % (3280530)Instructions burned: 7 (million)
% 3.48/1.38 % (3280530)------------------------------
% 3.48/1.38 % (3280530)------------------------------
% 3.48/1.38 % (3280522)Success in time 0.43 s
% 3.48/1.38 % Vampire exiting
%------------------------------------------------------------------------------