%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n007.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 12:15:35 PM UTC 2026
% Result : Theorem 2.62s 1.32s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 9 unt; 0 def)
% Number of atoms : 190 ( 37 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 249 ( 104 ~; 97 |; 40 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 50 !; 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(f46,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,
( 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(f52,plain,
( xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp) ),
inference(flattening,[],[f51]) ).
fof(f53,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,[],[f46]) ).
fof(f68,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f69,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f73,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f72]) ).
fof(f74,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(f75,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,[],[f74]) ).
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,[],[f73]) ).
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(sK2(X0,X1))
& sdtasdt0(X0,sK2(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f116]) ).
fof(f129,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f130,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f131,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f139,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f140,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f52]) ).
fof(f146,plain,
! [X0] :
( sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,xn) ),
inference(cnf_transformation,[],[f53]) ).
fof(f163,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f167,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f168,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,[],[f75]) ).
fof(f211,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f167]) ).
fof(f236,plain,
( sdtasdt0(xn,xn) != sdtasdt0(xn,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ doDivides0(xp,xn) ),
inference(superposition,[],[f146,f139]) ).
fof(f239,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ doDivides0(xp,xn) ),
inference(trivial_inequality_removal,[],[f236]) ).
fof(f462,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f211,f163]) ).
fof(f469,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f462,f139]) ).
fof(f476,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(forward_subsumption_resolution,[],[f469,f129]) ).
fof(f2070,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,xn)
| ~ isPrime0(xp)
| doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f476,f168]) ).
fof(f2072,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(duplicate_literal_removal,[],[f2070]) ).
fof(f2074,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f2072,f239]) ).
fof(f2076,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f2074,f140]) ).
fof(f2078,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f2076,f131]) ).
fof(f2079,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(forward_subsumption_resolution,[],[f2078,f129]) ).
fof(f2080,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f2079,f163]) ).
fof(f2081,plain,
~ aNaturalNumber0(xm),
inference(duplicate_literal_removal,[],[f2080]) ).
fof(f2082,plain,
$false,
inference(forward_subsumption_resolution,[],[f2081,f130]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.10/0.37 % Computer : n007.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 20:17:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.62/1.32 % (1754859)Detected formulas, will run a generic FOF schedule.
% 2.62/1.32 % (1754868)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2143214978:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.32 % (1754868)First to succeed.
% 2.62/1.32 % (1754868)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1754859"
% 2.62/1.32 % (1754869)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3815015219:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.32 % (1754864)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=1197945872:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.32 % (1754867)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2511194119:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.32 % (1754866)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=4053685293:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.32 % (1754865)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=806369301:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.32 % (1754870)dis-21_1_sil=8000:lcm=predicate:random_seed=3085672962: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)
% 2.62/1.32 % (1754867)Also succeeded, but the first one will report.
% 2.62/1.32 % (1754870)Instruction limit reached!
% 2.62/1.32 % (1754870)------------------------------
% 2.62/1.32 % (1754870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (1754870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (1754870)CaDiCaL version: 2.1.3
% 2.62/1.32 % (1754870)Termination reason: Instruction limit
% 2.62/1.32 % (1754870)Termination phase: Saturation
% 2.62/1.32 % (1754870)Time elapsed: 0.079 s
% 2.62/1.32 % (1754870)Peak memory usage: 91 MB
% 2.62/1.32 % (1754870)Instructions burned: 130 (million)
% 2.62/1.32 % (1754869)Instruction limit reached!
% 2.62/1.32 % (1754869)------------------------------
% 2.62/1.32 % (1754869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (1754869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (1754869)CaDiCaL version: 2.1.3
% 2.62/1.32 % (1754869)Termination reason: Instruction limit
% 2.62/1.32 % (1754869)Termination phase: Saturation
% 2.62/1.32 % (1754869)Time elapsed: 0.099 s
% 2.62/1.32 % (1754869)Peak memory usage: 90 MB
% 2.62/1.32 % (1754869)Instructions burned: 140 (million)
% 2.62/1.32 % (1754868)Refutation found. Thanks to Tanya!
% 2.62/1.32 % SZS status Theorem for theBenchmark
% 2.62/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.32 % (1754868)------------------------------
% 2.62/1.32 % (1754868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (1754868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (1754868)CaDiCaL version: 2.1.3
% 2.62/1.32 % (1754868)Termination reason: Refutation
% 2.62/1.32 % (1754868)Time elapsed: 0.022 s
% 2.62/1.32 % (1754868)Peak memory usage: 89 MB
% 2.62/1.32 % (1754868)Instructions burned: 68 (million)
% 2.62/1.32 % (1754868)------------------------------
% 2.62/1.32 % (1754868)------------------------------
% 2.62/1.32 % (1754859)Success in time 0.285 s
% 2.62/1.32 % Vampire exiting
%------------------------------------------------------------------------------