%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM523+3 : 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 : n016.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 12:24:39 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 12 unt; 3 def)
% Number of atoms : 227 ( 35 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 276 ( 112 ~; 113 |; 40 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 49 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
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(f39,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( isPrime0(X2)
& doDivides0(X2,sdtasdt0(X0,X1)) )
=> ( doDivides0(X2,X0)
| doDivides0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPDP) ).
fof(f40,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(f43,axiom,
( xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(f44,conjecture,
( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtasdt0(xn,xn)) )
& ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtasdt0(xn,xn)) )
& ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f48,plain,
~ ( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtasdt0(xn,xn)) )
& ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn) ) ),
inference(rectify,[],[f45]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f51]) ).
fof(f95,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f96,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f95]) ).
fof(f113,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f114,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f113]) ).
fof(f117,plain,
( xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp) ),
inference(ennf_transformation,[],[f43]) ).
fof(f118,plain,
( xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xn) != sdtasdt0(xp,X0) )
& ~ doDivides0(xp,sdtasdt0(xn,xn)) )
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xn) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f125,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,[],[f96]) ).
fof(f126,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,[],[f125]) ).
fof(f127,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))],[f126]) ).
fof(f140,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f185,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f204,plain,
! [X2,X0,X1] :
( ~ doDivides0(X2,sdtasdt0(X0,X1))
| doDivides0(X2,X1)
| ~ isPrime0(X2)
| doDivides0(X2,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f208,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f209,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f210,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f218,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f219,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f118]) ).
fof(f223,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(cnf_transformation,[],[f119]) ).
fof(f233,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f185]) ).
fof(f241,definition,
( spl6_1
<=> doDivides0(xp,xn) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f243,plain,
( ~ doDivides0(xp,xn)
| spl6_1 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f245,definition,
( spl6_2
<=> doDivides0(xp,sdtasdt0(xn,xn)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f246,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f223,f245,f241]) ).
fof(f332,definition,
( spl6_9
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
fof(f333,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f334,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| spl6_9 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f345,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| spl6_9 ),
inference(resolution,[],[f334,f140]) ).
fof(f346,plain,
( ~ aNaturalNumber0(xm)
| spl6_9 ),
inference(duplicate_literal_removal,[],[f345]) ).
fof(f347,plain,
( $false
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f346,f209]) ).
fof(f348,plain,
spl6_9,
inference(avatar_contradiction_clause,[],[f347]) ).
fof(f589,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f233,f140]) ).
fof(f615,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f589,f218]) ).
fof(f617,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f615,f333]) ).
fof(f625,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f617,f208]) ).
fof(f632,plain,
( spl6_2
| ~ spl6_9 ),
inference(avatar_split_clause,[],[f625,f332,f245]) ).
fof(f1690,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl6_2 ),
inference(resolution,[],[f204,f246]) ).
fof(f1704,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl6_2 ),
inference(duplicate_literal_removal,[],[f1690]) ).
fof(f1712,plain,
( ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f1704,f243]) ).
fof(f1717,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f1712,f219]) ).
fof(f1720,plain,
( ~ aNaturalNumber0(xp)
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f1717,f210]) ).
fof(f1721,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f1720,f208]) ).
fof(f1722,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f1721]) ).
cnf(s1,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f248]) ).
cnf(s11,plain,
spl6_9,
inference(sat_conversion,[],[f348]) ).
cnf(s18,plain,
( spl6_2
| ~ spl6_9 ),
inference(sat_conversion,[],[f632]) ).
cnf(s21,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f1722]) ).
cnf(s22,plain,
spl6_2,
inference(rat,[],[s18,s11]) ).
cnf(s23,plain,
spl6_1,
inference(rat,[],[s21,s22]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s1,s22,s23]) ).
fof(f1723,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM523+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:24:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.41 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
% 0.17/0.49 % (2964635)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (2964645)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=331569555:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (2964641)% WARNING: option uhcvi not known.
% 0.17/0.49 % (2964640)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1461330583_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (2964642)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1655416794:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (2964641)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1014041736:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (2964643)dis+10_1_sil=32000:sp=arity:random_seed=1086700297:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (2964644)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2802872948:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (2964646)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3602310332:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % Detected minimum model sizes of [3]
% 0.17/0.49 % Detected maximum model sizes of [max]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (2964643) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2964635-2964643"...
% 0.17/0.49 % (2964643)...printing done.
% 0.17/0.49 % (2964645)Instruction limit reached!
% 0.17/0.49 % (2964645)------------------------------
% 0.17/0.49 % (2964645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (2964645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (2964645)CaDiCaL version: 2.1.3
% 0.17/0.49 % (2964645)Termination reason: Instruction limit
% 0.17/0.49 % (2964645)Termination phase: Saturation
% 0.17/0.49 % (2964645)Time elapsed: 0.041 s
% 0.17/0.49 % (2964645)Peak memory usage: 12 MB
% 0.17/0.49 % (2964645)Instructions burned: 133 (million)
% 0.17/0.49 % (2964643)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (2964643)------------------------------
% 0.17/0.49 % (2964643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (2964643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (2964643)CaDiCaL version: 2.1.3
% 0.17/0.49 % (2964643)Termination reason: Refutation
% 0.17/0.49 % (2964643)Time elapsed: 0.031 s
% 0.17/0.49 % (2964643)Peak memory usage: 13 MB
% 0.17/0.49 % (2964643)Instructions burned: 51 (million)
% 0.17/0.49 % (2964635)Success in time 0.07 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------