%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM427+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 : n019.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 12:15:08 PM UTC 2026
% Result : Theorem 2.68s 1.34s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 30 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 28 ( 13 ~; 9 |; 5 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 7 ( 5 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f23,axiom,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__747) ).
fof(f24,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__767) ).
fof(f25,conjecture,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f26,negated_conjecture,
~ ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f28,plain,
( ! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xb,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(ennf_transformation,[],[f26]) ).
fof(f37,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f69,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f23]) ).
fof(f70,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(cnf_transformation,[],[f24]) ).
fof(f73,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f89,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f132,plain,
( sdtpldt0(xb,smndt0(xa)) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(smndt0(xn)) ),
inference(superposition,[],[f73,f70]) ).
fof(f134,plain,
~ aInteger0(smndt0(xn)),
inference(trivial_inequality_removal,[],[f132]) ).
fof(f136,plain,
~ aInteger0(xn),
inference(resolution,[],[f134,f89]) ).
fof(f137,plain,
$false,
inference(forward_subsumption_resolution,[],[f136,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n019.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 19:52:03 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.68/1.34 % (3368922)Detected formulas, will run a generic FOF schedule.
% 2.68/1.34 % (3368931)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1978254234:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.34 % (3368931)First to succeed.
% 2.68/1.34 % (3368931)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3368922"
% 2.68/1.34 % (3368927)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=487981921:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.34 % (3368928)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=3745801190:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.34 % (3368930)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=159731884:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.34 % (3368929)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=3547706297:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.34 % (3368930)Also succeeded, but the first one will report.
% 2.68/1.34 % (3368933)dis-21_1_sil=8000:lcm=predicate:random_seed=1041282322: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)
% 2.68/1.34 % (3368932)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1160607507:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.34 % (3368933)Also succeeded, but the first one will report.
% 2.68/1.34 % (3368932)Also succeeded, but the first one will report.
% 2.68/1.34 % (3368931)Refutation found. Thanks to Tanya!
% 2.68/1.34 % SZS status Theorem for theBenchmark
% 2.68/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.34 % (3368931)------------------------------
% 2.68/1.34 % (3368931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (3368931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (3368931)CaDiCaL version: 2.1.3
% 2.68/1.34 % (3368931)Termination reason: Refutation
% 2.68/1.34 % (3368931)Time elapsed: 0.002 s
% 2.68/1.34 % (3368931)Peak memory usage: 88 MB
% 2.68/1.34 % (3368931)Instructions burned: 3 (million)
% 2.68/1.34 % (3368931)------------------------------
% 2.68/1.34 % (3368931)------------------------------
% 2.68/1.34 % (3368922)Success in time 0.291 s
% 2.68/1.34 % Vampire exiting
%------------------------------------------------------------------------------