%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM482+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:24:29 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 11 unt; 1 def)
% Number of atoms : 118 ( 17 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 136 ( 58 ~; 50 |; 19 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 35 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f38,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
fof(f41,conjecture,
( isPrime0(xk)
=> ? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
~ ( isPrime0(xk)
=> ? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f47]) ).
fof(f58,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f91,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f92,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f91]) ).
fof(f109,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ isPrime0(X0) )
& isPrime0(xk) ),
inference(ennf_transformation,[],[f42]) ).
fof(f115,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f92]) ).
fof(f116,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f116]) ).
fof(f127,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f129,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f137,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f58]) ).
fof(f174,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f190,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f196,plain,
isPrime0(xk),
inference(cnf_transformation,[],[f109]) ).
fof(f197,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f204,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f174]) ).
fof(f212,definition,
( spl4_1
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f213,plain,
( aNaturalNumber0(sz10)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f229,plain,
spl4_1,
inference(avatar_split_clause,[],[f127,f212]) ).
fof(f240,plain,
xk = sdtasdt0(xk,sz10),
inference(resolution,[],[f137,f190]) ).
fof(f385,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f204,f129]) ).
fof(f398,plain,
( doDivides0(xk,xk)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[],[f385,f240]) ).
fof(f410,plain,
( doDivides0(xk,xk)
| ~ aNaturalNumber0(xk)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f398,f213]) ).
fof(f418,plain,
( doDivides0(xk,xk)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f410,f190]) ).
fof(f426,plain,
( ~ aNaturalNumber0(xk)
| ~ isPrime0(xk)
| ~ spl4_1 ),
inference(resolution,[],[f418,f197]) ).
fof(f429,plain,
( ~ isPrime0(xk)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f426,f190]) ).
fof(f430,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f429,f196]) ).
fof(f431,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f430]) ).
cnf(s3,plain,
spl4_1,
inference(sat_conversion,[],[f229]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f431]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5]) ).
fof(f432,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM482+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 20:06:45 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.47 % (2364089)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (2364099)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=21670833:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (2364095)% WARNING: option uhcvi not known.
% 0.16/0.47 % (2364094)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1406456599_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (2364095)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1510038944:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (2364097)dis+10_1_sil=32000:sp=arity:random_seed=1682603161:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (2364096)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3118277364:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (2364098)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2816763307:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (2364100)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1573357649:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % Detected minimum model sizes of [3]
% 0.16/0.47 % Detected maximum model sizes of [max]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (2364097) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2364089-2364097"...
% 0.16/0.47 % (2364097)...printing done.
% 0.16/0.47 % (2364097)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2364097)------------------------------
% 0.16/0.47 % (2364097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2364097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2364097)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2364097)Termination reason: Refutation
% 0.16/0.47 % (2364097)Time elapsed: 0.008 s
% 0.16/0.47 % (2364097)Peak memory usage: 12 MB
% 0.16/0.47 % (2364097)Instructions burned: 11 (million)
% 0.16/0.47 % (2364089)Success in time 0.046 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------