%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM504+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 : n011.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 12:24:34 PM UTC 2026
% Result : ContradictoryAxioms 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 15 unt; 0 def)
% Number of atoms : 152 ( 45 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 171 ( 63 ~; 50 |; 52 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 30 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f51,axiom,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm) )
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xp,xm),X0) = sdtasdt0(xp,xk) )
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).
fof(f55,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f41]) ).
fof(f59,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm) )
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X1) )
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(rectify,[],[f51]) ).
fof(f61,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f64,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f63]) ).
fof(f91,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f92,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f91]) ).
fof(f129,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f130,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(flattening,[],[f129]) ).
fof(f140,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f141,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f168,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f204,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f241,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK10),
inference(cnf_transformation,[],[f130]) ).
fof(f242,plain,
aNaturalNumber0(sK10),
inference(cnf_transformation,[],[f130]) ).
fof(f260,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f283,plain,
sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK18),
inference(cnf_transformation,[],[f59]) ).
fof(f284,plain,
aNaturalNumber0(sK18),
inference(cnf_transformation,[],[f59]) ).
fof(f287,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[],[f59]) ).
fof(f289,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f59]) ).
fof(f290,plain,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(cnf_transformation,[],[f59]) ).
fof(f305,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,sK10),
inference(forward_demodulation,[],[f241,f260]) ).
fof(f484,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK10) ),
inference(superposition,[],[f141,f305]) ).
fof(f485,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sK10) ),
inference(forward_subsumption_resolution,[],[f484,f204]) ).
fof(f488,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[],[f485,f242]) ).
fof(f501,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK18) ),
inference(superposition,[],[f140,f283]) ).
fof(f502,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f501,f284]) ).
fof(f503,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(forward_demodulation,[],[f502,f260]) ).
fof(f504,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(forward_subsumption_resolution,[],[f503,f488]) ).
fof(f1081,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(resolution,[],[f168,f289]) ).
fof(f1092,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(forward_subsumption_resolution,[],[f1081,f504]) ).
fof(f1096,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f1092,f290]) ).
fof(f1098,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_demodulation,[],[f1096,f260]) ).
fof(f1100,plain,
~ aNaturalNumber0(sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[],[f1098,f287]) ).
fof(f1102,plain,
~ aNaturalNumber0(sdtasdt0(xp,xk)),
inference(forward_demodulation,[],[f1100,f260]) ).
fof(f1104,plain,
$false,
inference(forward_subsumption_resolution,[],[f1102,f488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM504+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42 % Computer : n011.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 27 20:13:45 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.46 Running first-order model finding
% 0.14/0.46 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
% 0.17/0.51 % (2730081)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (2730094)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1954142771:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % (2730091)% WARNING: option uhcvi not known.
% 0.17/0.51 % (2730093)dis+10_1_sil=32000:sp=arity:random_seed=4042638547:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (2730091)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3406587175:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (2730090)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1407816702_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % (2730096)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2422489125:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % (2730092)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1387150524:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (2730095)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1821808513:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % (2730094) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2730081-2730094"...
% 0.17/0.51 % (2730094)...printing done.
% 0.17/0.51 % (2730094)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status ContradictoryAxioms for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (2730094)------------------------------
% 0.17/0.51 % (2730094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (2730094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (2730094)CaDiCaL version: 2.1.3
% 0.17/0.51 % (2730094)Termination reason: Refutation
% 0.17/0.51 % (2730094)Time elapsed: 0.013 s
% 0.17/0.51 % (2730094)Peak memory usage: 12 MB
% 0.17/0.51 % (2730094)Instructions burned: 42 (million)
% 0.17/0.51 % (2730081)Success in time 0.043 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------