%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM429+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 : n008.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 3.44s 1.46s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 5 unt; 1 def)
% Number of atoms : 45 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 40 ( 11 ~; 5 |; 23 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 14 ( 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc)) )
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__853) ).
fof(f24,conjecture,
? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,plain,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ? [X1] :
( aInteger0(X1)
& sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,X1) )
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(rectify,[],[f23]) ).
fof(f57,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(ennf_transformation,[],[f25]) ).
fof(f63,plain,
( aInteger0(sK1)
& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK1)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aInteger0(sK2)
& sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,sK2)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f27]) ).
fof(f106,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK1),
inference(cnf_transformation,[],[f63]) ).
fof(f107,plain,
aInteger0(sK1),
inference(cnf_transformation,[],[f63]) ).
fof(f108,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f111,definition,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ3_eqProxy])],[equality_proxy_definition]) ).
fof(f136,plain,
sQ3_eqProxy(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xq,sK1)),
inference(equality_proxy_replacement,[],[f106,f111]) ).
fof(f138,plain,
! [X0] :
( ~ sQ3_eqProxy(sdtasdt0(xq,X0),sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(X0) ),
inference(equality_proxy_replacement,[],[f108,f111]) ).
fof(f140,plain,
! [X0,X1] :
( sQ3_eqProxy(X1,X0)
| ~ sQ3_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f111]) ).
fof(f141,plain,
! [X0] :
( ~ sQ3_eqProxy(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xq,X0))
| ~ aInteger0(X0) ),
inference(resolution,[],[f140,f138]) ).
fof(f147,plain,
~ aInteger0(sK1),
inference(resolution,[],[f136,f141]) ).
fof(f148,plain,
$false,
inference(resolution,[],[f147,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM429+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 19:53:40 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.44/1.46 % (1560235)Detected formulas, will run a generic FOF schedule.
% 3.44/1.46 % (1560240)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=3313411974:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.46 % (1560246)dis-21_1_sil=8000:lcm=predicate:random_seed=4027511044: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)
% 3.44/1.46 % (1560244)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=624286365:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.46 % (1560243)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3563271589:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.46 % (1560241)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=4065149077:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.46 % (1560242)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=2291863707:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.46 % (1560246)First to succeed.
% 3.44/1.46 % (1560244)Also succeeded, but the first one will report.
% 3.44/1.46 % (1560246)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1560235"
% 3.44/1.46 % (1560245)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=192174511:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.46 % (1560243)Also succeeded, but the first one will report.
% 3.44/1.46 % (1560245)Also succeeded, but the first one will report.
% 3.44/1.46 % (1560246)Refutation found. Thanks to Tanya!
% 3.44/1.46 % SZS status Theorem for theBenchmark
% 3.44/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.46 % (1560246)------------------------------
% 3.44/1.46 % (1560246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.46 % (1560246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.46 % (1560246)CaDiCaL version: 2.1.3
% 3.44/1.46 % (1560246)Termination reason: Refutation
% 3.44/1.46 % (1560246)Time elapsed: 0.003 s
% 3.44/1.46 % (1560246)Peak memory usage: 88 MB
% 3.44/1.46 % (1560246)Instructions burned: 2 (million)
% 3.44/1.46 % (1560246)------------------------------
% 3.44/1.46 % (1560246)------------------------------
% 3.44/1.46 % (1560235)Success in time 0.403 s
% 3.44/1.46 % Vampire exiting
%------------------------------------------------------------------------------