%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM432+3 : 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 : n003.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 12:15:09 PM UTC 2026
% Result : Theorem 2.63s 1.35s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 41 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 41 ( 19 ~; 14 |; 7 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(f24,axiom,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__876) ).
fof(f25,axiom,
( aInteger0(xm)
& sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__899) ).
fof(f26,axiom,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__924) ).
fof(f27,conjecture,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xc)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xc)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f31,plain,
( ! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xc)) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
& ~ sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
inference(ennf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f51]) ).
fof(f79,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f24]) ).
fof(f81,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f82,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(cnf_transformation,[],[f26]) ).
fof(f85,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f108,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f157,plain,
( sdtpldt0(xa,smndt0(xc)) != sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(superposition,[],[f85,f82]) ).
fof(f159,plain,
~ aInteger0(sdtpldt0(xn,xm)),
inference(trivial_inequality_removal,[],[f157]) ).
fof(f161,plain,
( ~ aInteger0(xn)
| ~ aInteger0(xm) ),
inference(resolution,[],[f159,f108]) ).
fof(f162,plain,
~ aInteger0(xm),
inference(forward_subsumption_resolution,[],[f161,f79]) ).
fof(f163,plain,
$false,
inference(forward_subsumption_resolution,[],[f162,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM432+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 19:55:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.63/1.35 % (884675)Detected formulas, will run a generic FOF schedule.
% 2.63/1.35 % (884785)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=12558033:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.35 % (884785)First to succeed.
% 2.63/1.35 % (884785)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-884675"
% 2.63/1.35 % (884782)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=2244187742:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.35 % (884783)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=3880584240:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.35 % (884781)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=446763732:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.35 % (884784)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1289444227:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.35 % (884784)Also succeeded, but the first one will report.
% 2.63/1.35 % (884786)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=72651930:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.35 % (884787)dis-21_1_sil=8000:lcm=predicate:random_seed=1461012233: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)
% 2.63/1.35 % (884787)Also succeeded, but the first one will report.
% 2.63/1.35 % (884786)Also succeeded, but the first one will report.
% 2.63/1.35 % (884785)Refutation found. Thanks to Tanya!
% 2.63/1.35 % SZS status Theorem for theBenchmark
% 2.63/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.35 % (884785)------------------------------
% 2.63/1.35 % (884785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.35 % (884785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.35 % (884785)CaDiCaL version: 2.1.3
% 2.63/1.35 % (884785)Termination reason: Refutation
% 2.63/1.35 % (884785)Time elapsed: 0.002 s
% 2.63/1.35 % (884785)Peak memory usage: 88 MB
% 2.63/1.35 % (884785)Instructions burned: 4 (million)
% 2.63/1.35 % (884785)------------------------------
% 2.63/1.35 % (884785)------------------------------
% 2.63/1.35 % (884675)Success in time 0.29 s
% 2.63/1.35 % Vampire exiting
%------------------------------------------------------------------------------