%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM584+1 : 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 : 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 12:24:54 PM UTC 2026
% Result : Theorem 0.42s 0.50s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 19 unt; 1 def)
% Number of atoms : 93 ( 11 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 90 ( 36 ~; 31 |; 11 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f75,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f87,axiom,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4007) ).
fof(f88,axiom,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4024) ).
fof(f89,conjecture,
aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f90,negated_conjecture,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(flattening,[],[f90]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f176,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f177,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f176]) ).
fof(f221,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f251,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f307,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| slbdtsldtrb0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f177]) ).
fof(f350,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f352,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f375,plain,
xK = sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f87]) ).
fof(f376,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(cnf_transformation,[],[f88]) ).
fof(f377,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(cnf_transformation,[],[f91]) ).
fof(f404,plain,
! [X2,X3,X0] :
( ~ aElementOf0(sbrdtbr0(X3),szNzAzT0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| slbdtsldtrb0(X0,sbrdtbr0(X3)) != X2 ),
inference(equality_resolution,[],[f307]) ).
fof(f405,plain,
! [X3,X0] :
( ~ aSubsetOf0(X3,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X3),szNzAzT0)
| aElementOf0(X3,slbdtsldtrb0(X0,sbrdtbr0(X3))) ),
inference(equality_resolution,[],[f404]) ).
fof(f458,definition,
( spl21_5
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f459,plain,
( aSet0(xS)
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f466,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f221,f352]) ).
fof(f471,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[],[f466,f251]) ).
fof(f472,plain,
spl21_5,
inference(avatar_split_clause,[],[f471,f458]) ).
fof(f1916,plain,
( ~ aSet0(xS)
| ~ aElementOf0(sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),szNzAzT0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))))) ),
inference(resolution,[],[f405,f376]) ).
fof(f1927,plain,
( ~ aElementOf0(sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),szNzAzT0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))))
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f1916,f459]) ).
fof(f1931,plain,
( ~ aElementOf0(xK,szNzAzT0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))))
| ~ spl21_5 ),
inference(forward_demodulation,[],[f1927,f375]) ).
fof(f1934,plain,
( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))))
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f1931,f350]) ).
fof(f1937,plain,
( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
| ~ spl21_5 ),
inference(forward_demodulation,[],[f1934,f375]) ).
fof(f1940,plain,
( $false
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f1937,f377]) ).
fof(f1941,plain,
~ spl21_5,
inference(avatar_contradiction_clause,[],[f1940]) ).
cnf(s5,plain,
spl21_5,
inference(sat_conversion,[],[f472]) ).
cnf(s69,plain,
~ spl21_5,
inference(sat_conversion,[],[f1941]) ).
cnf(s85,plain,
$false,
inference(rat,[],[s5,s69]) ).
fof(f1944,plain,
$false,
inference(avatar_sat_refutation,[],[s85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM584+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n020.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 20:37:49 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41 Running first-order model finding
% 0.14/0.41 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
% 0.42/0.50 % (3725771)Will run a generic schedule for satisfiability detection.
% 0.42/0.50 % (3725782)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1999922034:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.42/0.50 % (3725777)% WARNING: option uhcvi not known.
% 0.42/0.50 % (3725776)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=610634237_2999 on theBenchmark for (2999ds/0Mi)
% 0.42/0.50 % (3725778)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=122884214:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.42/0.50 % (3725779)dis+10_1_sil=32000:sp=arity:random_seed=2588782083:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.42/0.50 % (3725780)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=731500092:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.42/0.50 % (3725781)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3484843406:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.42/0.50 % (3725777)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=719742428:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.42/0.50 % TRYING [1]
% 0.42/0.50 % TRYING [2]
% 0.42/0.50 % TRYING [3]
% 0.42/0.50 % (3725780) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3725771-3725780"...
% 0.42/0.50 % (3725780)...printing done.
% 0.42/0.50 % (3725780)Refutation found. Thanks to Tanya!
% 0.42/0.50 % SZS status Theorem for theBenchmark
% 0.42/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.42/0.50 % (3725780)------------------------------
% 0.42/0.50 % (3725780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.50 % (3725780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.50 % (3725780)CaDiCaL version: 2.1.3
% 0.42/0.50 % (3725780)Termination reason: Refutation
% 0.42/0.50 % (3725780)Time elapsed: 0.043 s
% 0.42/0.50 % (3725780)Peak memory usage: 13 MB
% 0.42/0.50 % (3725780)Instructions burned: 63 (million)
% 0.42/0.50 % (3725771)Success in time 0.079 s
% 0.42/0.50 % Vampire exiting
%------------------------------------------------------------------------------