%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM521+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 : n020.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 12:15:34 PM UTC 2026
% Result : Theorem 2.47s 1.23s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 137 ( 45 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 162 ( 70 ~; 56 |; 34 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 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 : 31 ( 19 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f42,axiom,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xn )
| sdtlseqdt0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f43,axiom,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xm )
| sdtlseqdt0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(f44,axiom,
~ ( xn != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
| sdtlseqdt0(xn,xp) )
& xm != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xp )
| sdtlseqdt0(xm,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f45,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f46,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f49,plain,
~ ( xn != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
| sdtlseqdt0(xn,xp) )
& xm != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtpldt0(xm,X1) )
| sdtlseqdt0(xm,xp) ) ),
inference(rectify,[],[f44]) ).
fof(f50,plain,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ),
inference(rectify,[],[f46]) ).
fof(f57,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtpldt0(xp,X0) )
& ~ sdtlseqdt0(xp,xn) ),
inference(ennf_transformation,[],[f42]) ).
fof(f58,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xm != sdtpldt0(xp,X0) )
& ~ sdtlseqdt0(xp,xm) ),
inference(ennf_transformation,[],[f43]) ).
fof(f59,plain,
( xn = xp
| ( ! [X0] :
( ~ aNaturalNumber0(X0)
| xp != sdtpldt0(xn,X0) )
& ~ sdtlseqdt0(xn,xp) )
| xm = xp
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| xp != sdtpldt0(xm,X1) )
& ~ sdtlseqdt0(xm,xp) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f60,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) )
& ~ doDivides0(xp,xn)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm) ),
inference(ennf_transformation,[],[f50]) ).
fof(f63,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f110,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f111,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f110]) ).
fof(f142,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f143,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f144,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f169,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f57]) ).
fof(f171,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f58]) ).
fof(f173,plain,
( xn = xp
| ~ sdtlseqdt0(xn,xp)
| xm = xp
| ~ sdtlseqdt0(xm,xp) ),
inference(cnf_transformation,[],[f59]) ).
fof(f178,plain,
! [X1] :
( xm != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f180,plain,
! [X0] :
( xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f185,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f187,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f234,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f257,plain,
( xn != xp
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f180,f185]) ).
fof(f258,plain,
( xm != xp
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f178,f185]) ).
fof(f259,plain,
( xm != xp
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f258,f187]) ).
fof(f260,plain,
( xn != xp
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f257,f187]) ).
fof(f261,plain,
xm != xp,
inference(forward_subsumption_resolution,[],[f259,f142]) ).
fof(f262,plain,
xn != xp,
inference(forward_subsumption_resolution,[],[f260,f142]) ).
fof(f301,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f234,f169]) ).
fof(f302,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f234,f171]) ).
fof(f303,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f302,f143]) ).
fof(f304,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f301,f144]) ).
fof(f305,plain,
sdtlseqdt0(xm,xp),
inference(forward_subsumption_resolution,[],[f303,f142]) ).
fof(f306,plain,
sdtlseqdt0(xn,xp),
inference(forward_subsumption_resolution,[],[f304,f142]) ).
fof(f434,plain,
( ~ sdtlseqdt0(xn,xp)
| xm = xp
| ~ sdtlseqdt0(xm,xp) ),
inference(forward_subsumption_resolution,[],[f173,f262]) ).
fof(f435,plain,
( xm = xp
| ~ sdtlseqdt0(xm,xp) ),
inference(forward_subsumption_resolution,[],[f434,f306]) ).
fof(f436,plain,
~ sdtlseqdt0(xm,xp),
inference(forward_subsumption_resolution,[],[f435,f261]) ).
fof(f437,plain,
$false,
inference(forward_subsumption_resolution,[],[f436,f305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM521+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:19:50 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.47/1.23 % (3717409)Detected formulas, will run a generic FOF schedule.
% 2.47/1.23 % (3717418)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1690979881:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.47/1.23 % (3717418)First to succeed.
% 2.47/1.23 % (3717418)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3717409"
% 2.47/1.23 % (3717414)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=184589667:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.47/1.23 % (3717417)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1155592095:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.47/1.23 % (3717415)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=858449504:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.47/1.23 % (3717416)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=744690988:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.47/1.23 % (3717419)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2020742457:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.47/1.23 % (3717419)Also succeeded, but the first one will report.
% 2.47/1.23 % (3717420)dis-21_1_sil=8000:lcm=predicate:random_seed=3878048474: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)
% 2.47/1.23 % (3717417)Also succeeded, but the first one will report.
% 2.47/1.23 % (3717420)Instruction limit reached!
% 2.47/1.23 % (3717420)------------------------------
% 2.47/1.23 % (3717420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.23 % (3717420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.23 % (3717420)CaDiCaL version: 2.1.3
% 2.47/1.23 % (3717420)Termination reason: Instruction limit
% 2.47/1.23 % (3717420)Termination phase: Saturation
% 2.47/1.23 % (3717420)Time elapsed: 0.079 s
% 2.47/1.23 % (3717420)Peak memory usage: 90 MB
% 2.47/1.23 % (3717420)Instructions burned: 129 (million)
% 2.47/1.23 % (3717418)Refutation found. Thanks to Tanya!
% 2.47/1.23 % SZS status Theorem for theBenchmark
% 2.47/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/1.23 % (3717418)------------------------------
% 2.47/1.23 % (3717418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.23 % (3717418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.23 % (3717418)CaDiCaL version: 2.1.3
% 2.47/1.23 % (3717418)Termination reason: Refutation
% 2.47/1.23 % (3717418)Time elapsed: 0.004 s
% 2.47/1.23 % (3717418)Peak memory usage: 88 MB
% 2.47/1.23 % (3717418)Instructions burned: 10 (million)
% 2.47/1.23 % (3717418)------------------------------
% 2.47/1.23 % (3717418)------------------------------
% 2.47/1.23 % (3717409)Success in time 0.274 s
% 2.47/1.23 % Vampire exiting
%------------------------------------------------------------------------------