%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM425+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:15:07 PM UTC 2026
% Result : Theorem 2.70s 1.35s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 1 def)
% Number of atoms : 29 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 5 |; 8 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__724) ).
fof(f23,conjecture,
? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f24,negated_conjecture,
~ ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f53,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f59,plain,
( aInteger0(sK1)
& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK1)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f22]) ).
fof(f96,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK1),
inference(cnf_transformation,[],[f59]) ).
fof(f97,plain,
aInteger0(sK1),
inference(cnf_transformation,[],[f59]) ).
fof(f98,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f101,definition,
! [X0,X1] :
( sQ2_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ2_eqProxy])],[equality_proxy_definition]) ).
fof(f125,plain,
sQ2_eqProxy(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xq,sK1)),
inference(equality_proxy_replacement,[],[f96,f101]) ).
fof(f126,plain,
! [X0] :
( ~ sQ2_eqProxy(sdtasdt0(xq,X0),sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(X0) ),
inference(equality_proxy_replacement,[],[f98,f101]) ).
fof(f128,plain,
! [X0,X1] :
( sQ2_eqProxy(X1,X0)
| ~ sQ2_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f101]) ).
fof(f129,plain,
! [X0] :
( ~ sQ2_eqProxy(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xq,X0))
| ~ aInteger0(X0) ),
inference(resolution,[],[f128,f126]) ).
fof(f134,plain,
~ aInteger0(sK1),
inference(resolution,[],[f125,f129]) ).
fof(f135,plain,
$false,
inference(resolution,[],[f134,f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM425+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 19:47:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.70/1.35 % (2897620)Detected formulas, will run a generic FOF schedule.
% 2.70/1.35 % (2897631)dis-21_1_sil=8000:lcm=predicate:random_seed=3441233227: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)
% 2.70/1.35 % (2897631)First to succeed.
% 2.70/1.35 % (2897631)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2897620"
% 2.70/1.35 % (2897628)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4142704664:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.35 % (2897627)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=1270034539:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.35 % (2897629)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4052339486:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.35 % (2897625)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=2330599111:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.35 % (2897626)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=1134943007:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.35 % (2897630)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2913695712:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.35 % (2897629)Also succeeded, but the first one will report.
% 2.70/1.35 % (2897630)Also succeeded, but the first one will report.
% 2.70/1.35 % (2897628)Also succeeded, but the first one will report.
% 2.70/1.35 % (2897631)Refutation found. Thanks to Tanya!
% 2.70/1.35 % SZS status Theorem for theBenchmark
% 2.70/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.35 % (2897631)------------------------------
% 2.70/1.35 % (2897631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.35 % (2897631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.35 % (2897631)CaDiCaL version: 2.1.3
% 2.70/1.35 % (2897631)Termination reason: Refutation
% 2.70/1.35 % (2897631)Time elapsed: 0.002 s
% 2.70/1.35 % (2897631)Peak memory usage: 88 MB
% 2.70/1.35 % (2897631)Instructions burned: 2 (million)
% 2.70/1.35 % (2897631)------------------------------
% 2.70/1.35 % (2897631)------------------------------
% 2.70/1.35 % (2897620)Success in time 0.298 s
% 2.70/1.35 % Vampire exiting
%------------------------------------------------------------------------------