%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM523+1 : 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 : n018.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 2.63s 1.38s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 11 unt; 0 def)
% Number of atoms : 151 ( 15 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 197 ( 90 ~; 79 |; 21 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 42 !; 5 ?)
% 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,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(f44,conjecture,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f50,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(ennf_transformation,[],[f45]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f62]) ).
fof(f64,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(f65,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,[],[f64]) ).
fof(f78,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f79,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f78]) ).
fof(f116,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,[],[f79]) ).
fof(f117,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,[],[f116]) ).
fof(f118,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))],[f117]) ).
fof(f125,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f126,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f127,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f129,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f130,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f43]) ).
fof(f131,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(cnf_transformation,[],[f50]) ).
fof(f141,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f142,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,[],[f65]) ).
fof(f159,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f196,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f159]) ).
fof(f346,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f196,f141]) ).
fof(f353,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f346,f129]) ).
fof(f360,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(forward_subsumption_resolution,[],[f353,f125]) ).
fof(f393,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ doDivides0(xp,xn) ),
inference(resolution,[],[f360,f131]) ).
fof(f394,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f393,f141]) ).
fof(f395,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xm) ),
inference(duplicate_literal_removal,[],[f394]) ).
fof(f396,plain,
~ doDivides0(xp,xn),
inference(forward_subsumption_resolution,[],[f395,f126]) ).
fof(f1004,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolution,[],[f142,f360]) ).
fof(f1024,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(duplicate_literal_removal,[],[f1004]) ).
fof(f1034,plain,
( ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(forward_subsumption_resolution,[],[f1024,f396]) ).
fof(f1039,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(forward_subsumption_resolution,[],[f1034,f130]) ).
fof(f1041,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(forward_subsumption_resolution,[],[f1039,f127]) ).
fof(f1042,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(forward_subsumption_resolution,[],[f1041,f125]) ).
fof(f1043,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f1042,f141]) ).
fof(f1044,plain,
~ aNaturalNumber0(xm),
inference(duplicate_literal_removal,[],[f1043]) ).
fof(f1045,plain,
$false,
inference(forward_subsumption_resolution,[],[f1044,f126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM523+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n018.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 20:22:09 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 2.63/1.38 % (2695788)Detected formulas, will run a generic FOF schedule.
% 2.63/1.38 % (2695797)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3490417968:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.38 % (2695797)First to succeed.
% 2.63/1.38 % (2695797)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2695788"
% 2.63/1.38 % (2695796)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3284410296:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.38 % (2695795)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=3150300989:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.38 % (2695793)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=2181052433:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.38 % (2695794)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=1770693604:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.38 % (2695796)Also succeeded, but the first one will report.
% 2.63/1.38 % (2695799)dis-21_1_sil=8000:lcm=predicate:random_seed=889365754: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)
% 2.63/1.38 % (2695798)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=201204201:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.38 % (2695799)Instruction limit reached!
% 2.63/1.38 % (2695799)------------------------------
% 2.63/1.38 % (2695799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.38 % (2695799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.38 % (2695799)CaDiCaL version: 2.1.3
% 2.63/1.38 % (2695799)Termination reason: Instruction limit
% 2.63/1.38 % (2695799)Termination phase: Saturation
% 2.63/1.38 % (2695799)Time elapsed: 0.078 s
% 2.63/1.38 % (2695799)Peak memory usage: 90 MB
% 2.63/1.38 % (2695799)Instructions burned: 130 (million)
% 2.63/1.38 % (2695798)Instruction limit reached!
% 2.63/1.38 % (2695798)------------------------------
% 2.63/1.38 % (2695798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.38 % (2695798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.38 % (2695798)CaDiCaL version: 2.1.3
% 2.63/1.38 % (2695798)Termination reason: Instruction limit
% 2.63/1.38 % (2695798)Termination phase: Saturation
% 2.63/1.38 % (2695798)Time elapsed: 0.090 s
% 2.63/1.38 % (2695798)Peak memory usage: 90 MB
% 2.63/1.38 % (2695798)Instructions burned: 140 (million)
% 2.63/1.38 % (2695797)Refutation found. Thanks to Tanya!
% 2.63/1.38 % SZS status Theorem for theBenchmark
% 2.63/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.38 % (2695797)------------------------------
% 2.63/1.38 % (2695797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.38 % (2695797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.38 % (2695797)CaDiCaL version: 2.1.3
% 2.63/1.38 % (2695797)Termination reason: Refutation
% 2.63/1.38 % (2695797)Time elapsed: 0.009 s
% 2.63/1.38 % (2695797)Peak memory usage: 88 MB
% 2.63/1.38 % (2695797)Instructions burned: 24 (million)
% 2.63/1.38 % (2695797)------------------------------
% 2.63/1.38 % (2695797)------------------------------
% 2.63/1.38 % (2695788)Success in time 0.294 s
% 2.63/1.38 % Vampire exiting
%------------------------------------------------------------------------------