%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM500+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 12:24:33 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 20 unt; 4 def)
% Number of atoms : 223 ( 60 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 235 ( 90 ~; 100 |; 29 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 39 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f38,axiom,
! [X0] :
( ( aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 )
=> ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f47,axiom,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
fof(f48,conjecture,
? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f53,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f54,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f53]) ).
fof(f101,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f101]) ).
fof(f113,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f114,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(ennf_transformation,[],[f38]) ).
fof(f116,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(flattening,[],[f115]) ).
fof(f120,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ isPrime0(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f121,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f125,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2 ),
inference(cnf_transformation,[],[f102]) ).
fof(f184,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 != X0
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f185,plain,
! [X0] :
( isPrime0(sK3(X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz10 = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f186,plain,
! [X0] :
( doDivides0(sK3(X0),X0)
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz10 = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f187,plain,
! [X0] :
( aNaturalNumber0(sK3(X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz10 = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f188,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f189,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f190,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f192,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f193,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f200,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f203,plain,
sz10 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f204,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f205,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f213,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f171]) ).
fof(f215,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f184]) ).
fof(f228,definition,
( spl4_3
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f230,plain,
( ~ isPrime0(sz00)
| spl4_3 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl4_4
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f235,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f215,f232,f228]) ).
fof(f237,plain,
spl4_4,
inference(avatar_split_clause,[],[f121,f232]) ).
fof(f360,definition,
( spl4_5
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f361,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f362,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_5 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f368,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_5 ),
inference(resolution,[],[f362,f125]) ).
fof(f369,plain,
( ~ aNaturalNumber0(xm)
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f368,f190]) ).
fof(f370,plain,
( $false
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f369,f189]) ).
fof(f371,plain,
spl4_5,
inference(avatar_contradiction_clause,[],[f370]) ).
fof(f372,plain,
! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(X0)
| sz10 = X0
| ~ doDivides0(sK3(X0),xk)
| ~ aNaturalNumber0(sK3(X0)) ),
inference(resolution,[],[f185,f205]) ).
fof(f373,plain,
! [X0] :
( ~ doDivides0(sK3(X0),xk)
| ~ aNaturalNumber0(X0)
| sz10 = X0
| sz00 = X0 ),
inference(forward_subsumption_resolution,[],[f372,f187]) ).
fof(f460,definition,
( spl4_11
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f461,plain,
( sz00 != xp
| spl4_11 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f462,plain,
( sz00 = xp
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f505,plain,
( isPrime0(sz00)
| ~ spl4_11 ),
inference(superposition,[],[f193,f462]) ).
fof(f526,plain,
( $false
| spl4_3
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f505,f230]) ).
fof(f527,plain,
( spl4_3
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f526]) ).
fof(f612,plain,
( sz00 = xk
| ~ aNaturalNumber0(xk)
| sz10 = xk
| ~ aNaturalNumber0(xk)
| sz10 = xk
| sz00 = xk ),
inference(resolution,[],[f186,f373]) ).
fof(f615,plain,
( sz00 = xk
| ~ aNaturalNumber0(xk)
| sz10 = xk ),
inference(duplicate_literal_removal,[],[f612]) ).
fof(f617,plain,
( ~ aNaturalNumber0(xk)
| sz10 = xk ),
inference(forward_subsumption_resolution,[],[f615,f204]) ).
fof(f618,plain,
~ aNaturalNumber0(xk),
inference(forward_subsumption_resolution,[],[f617,f203]) ).
fof(f899,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(resolution,[],[f213,f192]) ).
fof(f907,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(forward_subsumption_resolution,[],[f899,f188]) ).
fof(f909,plain,
( sz00 = xp
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f907,f361]) ).
fof(f910,plain,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl4_5
| spl4_11 ),
inference(forward_subsumption_resolution,[],[f909,f461]) ).
fof(f911,plain,
( aNaturalNumber0(xk)
| ~ spl4_5
| spl4_11 ),
inference(forward_demodulation,[],[f910,f200]) ).
fof(f912,plain,
( $false
| ~ spl4_5
| spl4_11 ),
inference(forward_subsumption_resolution,[],[f911,f618]) ).
fof(f913,plain,
( ~ spl4_5
| spl4_11 ),
inference(avatar_contradiction_clause,[],[f912]) ).
cnf(s2,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f235]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f237]) ).
cnf(s6,plain,
spl4_5,
inference(sat_conversion,[],[f371]) ).
cnf(s14,plain,
( spl4_3
| ~ spl4_11 ),
inference(sat_conversion,[],[f527]) ).
cnf(s24,plain,
( ~ spl4_5
| spl4_11 ),
inference(sat_conversion,[],[f913]) ).
cnf(s25,plain,
spl4_11,
inference(rat,[],[s24,s6]) ).
cnf(s27,plain,
spl4_3,
inference(rat,[],[s14,s25]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s2,s4,s27]) ).
fof(f914,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM500+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:13:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 % (1278380)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (1278389)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1880281763:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (1278386)% WARNING: option uhcvi not known.
% 0.17/0.46 % (1278388)dis+10_1_sil=32000:sp=arity:random_seed=2889362644:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (1278387)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3078748067:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (1278385)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3059295104_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (1278386)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3177539569:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (1278389) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1278380-1278389"...
% 0.17/0.46 % (1278389)...printing done.
% 0.17/0.46 % Detected minimum model sizes of [3]
% 0.17/0.46 % Detected maximum model sizes of [max]
% 0.17/0.46 % (1278389)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (1278389)------------------------------
% 0.17/0.46 % (1278389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (1278389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (1278389)CaDiCaL version: 2.1.3
% 0.17/0.46 % (1278389)Termination reason: Refutation
% 0.17/0.46 % (1278389)Time elapsed: 0.011 s
% 0.17/0.46 % (1278389)Peak memory usage: 13 MB
% 0.17/0.46 % (1278389)Instructions burned: 30 (million)
% 0.17/0.46 % (1278380)Success in time 0.048 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------