%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM633+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 : n004.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 12:25:06 PM UTC 2026
% Result : Theorem 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 10 unt; 1 def)
% Number of atoms : 217 ( 32 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 249 ( 65 ~; 54 |; 100 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 50 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).
fof(f96,axiom,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
fof(f98,axiom,
( ! [X0] :
( aElementOf0(X0,xO)
=> aElementOf0(X0,xS) )
& aSubsetOf0(xO,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).
fof(f99,conjecture,
( ! [X0] :
( ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xO) ) )
| aSubsetOf0(X0,xO) )
& sbrdtbr0(X0) = xK )
| aElementOf0(X0,slbdtsldtrb0(xO,xK)) )
=> ( ~ ( ~ ? [X1] : aElementOf0(X1,X0)
| X0 = slcrc0 )
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(X0,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) ) )
=> ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xK
& aElementOf0(X2,slbdtsldtrb0(X1,xK)) )
=> sdtlpdtrp0(xc,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f100,negated_conjecture,
~ ( ! [X0] :
( ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xO) ) )
| aSubsetOf0(X0,xO) )
& sbrdtbr0(X0) = xK )
| aElementOf0(X0,slbdtsldtrb0(xO,xK)) )
=> ( ~ ( ~ ? [X1] : aElementOf0(X1,X0)
| X0 = slcrc0 )
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(X0,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) ) )
=> ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xK
& aElementOf0(X2,slbdtsldtrb0(X1,xK)) )
=> sdtlpdtrp0(xc,X2) = X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f99]) ).
fof(f113,plain,
~ ( ! [X0] :
( ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xO) ) )
| aSubsetOf0(X0,xO) )
& sbrdtbr0(X0) = xK )
| aElementOf0(X0,slbdtsldtrb0(xO,xK)) )
=> ( ~ ( ~ ? [X2] : aElementOf0(X2,X0)
| X0 = slcrc0 )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(X3,szNzAzT0) )
& aSubsetOf0(X0,szNzAzT0)
& ! [X4] :
( aElementOf0(X4,X0)
=> aElementOf0(X4,xS) )
& aSubsetOf0(X0,xS)
& ! [X5] :
( aElementOf0(X5,X0)
=> aElementOf0(X5,xS) )
& aSubsetOf0(X0,xS)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) ) )
=> ? [X6] :
( aElementOf0(X6,xT)
& ? [X7] :
( ( ( aSet0(X7)
& ! [X8] :
( aElementOf0(X8,X7)
=> aElementOf0(X8,xS) ) )
| aSubsetOf0(X7,xS) )
& isCountable0(X7)
& ! [X9] :
( ( aSet0(X9)
& ! [X10] :
( aElementOf0(X10,X9)
=> aElementOf0(X10,X7) )
& aSubsetOf0(X9,X7)
& xK = sbrdtbr0(X9)
& aElementOf0(X9,slbdtsldtrb0(X7,xK)) )
=> sdtlpdtrp0(xc,X9) = X6 ) ) ) ),
inference(rectify,[],[f100]) ).
fof(f252,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xO) )
& aSubsetOf0(xO,xS) ),
inference(ennf_transformation,[],[f98]) ).
fof(f253,plain,
( ! [X6] :
( ~ aElementOf0(X6,xT)
| ! [X7] :
( ( ( ~ aSet0(X7)
| ? [X8] :
( ~ aElementOf0(X8,xS)
& aElementOf0(X8,X7) ) )
& ~ aSubsetOf0(X7,xS) )
| ~ isCountable0(X7)
| ? [X9] :
( sdtlpdtrp0(xc,X9) != X6
& aSet0(X9)
& ! [X10] :
( aElementOf0(X10,X7)
| ~ aElementOf0(X10,X9) )
& aSubsetOf0(X9,X7)
& xK = sbrdtbr0(X9)
& aElementOf0(X9,slbdtsldtrb0(X7,xK)) ) ) )
& ! [X0] :
( ( ? [X2] : aElementOf0(X2,X0)
& slcrc0 != X0
& ! [X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,X0) )
& aSubsetOf0(X0,szNzAzT0)
& ! [X4] :
( aElementOf0(X4,xS)
| ~ aElementOf0(X4,X0) )
& aSubsetOf0(X0,xS)
& ! [X5] :
( aElementOf0(X5,xS)
| ~ aElementOf0(X5,X0) )
& aSubsetOf0(X0,xS)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) )
| ( ( ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xO)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xO) )
| sbrdtbr0(X0) != xK )
& ~ aElementOf0(X0,slbdtsldtrb0(xO,xK)) ) ) ),
inference(ennf_transformation,[],[f113]) ).
fof(f254,plain,
( ! [X6] :
( ~ aElementOf0(X6,xT)
| ! [X7] :
( ( ( ~ aSet0(X7)
| ? [X8] :
( ~ aElementOf0(X8,xS)
& aElementOf0(X8,X7) ) )
& ~ aSubsetOf0(X7,xS) )
| ~ isCountable0(X7)
| ? [X9] :
( sdtlpdtrp0(xc,X9) != X6
& aSet0(X9)
& ! [X10] :
( aElementOf0(X10,X7)
| ~ aElementOf0(X10,X9) )
& aSubsetOf0(X9,X7)
& xK = sbrdtbr0(X9)
& aElementOf0(X9,slbdtsldtrb0(X7,xK)) ) ) )
& ! [X0] :
( ( ? [X2] : aElementOf0(X2,X0)
& slcrc0 != X0
& ! [X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,X0) )
& aSubsetOf0(X0,szNzAzT0)
& ! [X4] :
( aElementOf0(X4,xS)
| ~ aElementOf0(X4,X0) )
& aSubsetOf0(X0,xS)
& ! [X5] :
( aElementOf0(X5,xS)
| ~ aElementOf0(X5,X0) )
& aSubsetOf0(X0,xS)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) )
| ( ( ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xO)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xO) )
| sbrdtbr0(X0) != xK )
& ~ aElementOf0(X0,slbdtsldtrb0(xO,xK)) ) ) ),
inference(flattening,[],[f253]) ).
fof(f751,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f94]) ).
fof(f761,plain,
isCountable0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f772,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[],[f252]) ).
fof(f788,plain,
! [X6,X7] :
( ~ isCountable0(X7)
| aElementOf0(sK59(X6,X7),slbdtsldtrb0(X7,xK))
| ~ aSubsetOf0(X7,xS)
| ~ aElementOf0(X6,xT) ),
inference(cnf_transformation,[],[f254]) ).
fof(f792,plain,
! [X6,X7] :
( ~ isCountable0(X7)
| sdtlpdtrp0(xc,sK59(X6,X7)) != X6
| ~ aSubsetOf0(X7,xS)
| ~ aElementOf0(X6,xT) ),
inference(cnf_transformation,[],[f254]) ).
fof(f807,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xO,xK))
| szDzizrdt0(xd) = sdtlpdtrp0(xc,X0) ),
inference(cnf_transformation,[],[f254]) ).
fof(f1162,plain,
! [X0] :
( aElementOf0(sK59(X0,xO),slbdtsldtrb0(xO,xK))
| ~ aSubsetOf0(xO,xS)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[],[f761,f788]) ).
fof(f1166,plain,
! [X0] :
( sdtlpdtrp0(xc,sK59(X0,xO)) != X0
| ~ aSubsetOf0(xO,xS)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[],[f761,f792]) ).
fof(f1167,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xc,sK59(X0,xO)) != X0 ),
inference(forward_subsumption_resolution,[],[f1166,f772]) ).
fof(f1171,plain,
! [X0] :
( aElementOf0(sK59(X0,xO),slbdtsldtrb0(xO,xK))
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f1162,f772]) ).
fof(f1424,plain,
szDzizrdt0(xd) != sdtlpdtrp0(xc,sK59(szDzizrdt0(xd),xO)),
inference(resolution,[],[f751,f1167]) ).
fof(f1888,definition,
( spl62_93
<=> aElementOf0(sK59(szDzizrdt0(xd),xO),slbdtsldtrb0(xO,xK)) ),
introduced(definition,[new_symbols(definition,[spl62_93])],[avatar_definition]) ).
fof(f1889,plain,
( aElementOf0(sK59(szDzizrdt0(xd),xO),slbdtsldtrb0(xO,xK))
| ~ spl62_93 ),
inference(avatar_component_clause,[],[f1888]) ).
fof(f1890,plain,
( ~ aElementOf0(sK59(szDzizrdt0(xd),xO),slbdtsldtrb0(xO,xK))
| spl62_93 ),
inference(avatar_component_clause,[],[f1888]) ).
fof(f1908,plain,
( ~ aElementOf0(szDzizrdt0(xd),xT)
| spl62_93 ),
inference(resolution,[],[f1890,f1171]) ).
fof(f1909,plain,
( $false
| spl62_93 ),
inference(forward_subsumption_resolution,[],[f1908,f751]) ).
fof(f1910,plain,
spl62_93,
inference(avatar_contradiction_clause,[],[f1909]) ).
fof(f1959,plain,
( szDzizrdt0(xd) = sdtlpdtrp0(xc,sK59(szDzizrdt0(xd),xO))
| ~ spl62_93 ),
inference(resolution,[],[f1889,f807]) ).
fof(f1966,plain,
( $false
| ~ spl62_93 ),
inference(forward_subsumption_resolution,[],[f1959,f1424]) ).
fof(f1967,plain,
~ spl62_93,
inference(avatar_contradiction_clause,[],[f1966]) ).
cnf(s128,plain,
spl62_93,
inference(sat_conversion,[],[f1910]) ).
cnf(s130,plain,
~ spl62_93,
inference(sat_conversion,[],[f1967]) ).
cnf(s133,plain,
$false,
inference(rat,[],[s128,s130]) ).
fof(f1970,plain,
$false,
inference(avatar_sat_refutation,[],[s133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM633+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 20:51:25 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 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
% 0.16/0.52 % (3868201)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (3868211)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1856096443:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % (3868207)% WARNING: option uhcvi not known.
% 0.16/0.52 % (3868207)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=638857511:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (3868206)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=781576331_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (3868208)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3540984939:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (3868209)dis+10_1_sil=32000:sp=arity:random_seed=1904065763:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (3868210)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=227876026:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (3868212)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1361425833:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % (3868211)Instruction limit reached!
% 0.16/0.52 % (3868211)------------------------------
% 0.16/0.52 % (3868211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3868211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3868211)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3868211)Termination reason: Instruction limit
% 0.16/0.52 % (3868211)Termination phase: Saturation
% 0.16/0.52 % (3868211)Time elapsed: 0.047 s
% 0.16/0.52 % (3868211)Peak memory usage: 14 MB
% 0.16/0.52 % (3868211)Instructions burned: 133 (million)
% 0.16/0.52 % (3868220)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1658284909:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % (3868210) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3868201-3868210"...
% 0.16/0.52 % (3868210)...printing done.
% 0.16/0.52 % (3868210)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Theorem for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (3868210)------------------------------
% 0.16/0.52 % (3868210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3868210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3868210)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3868210)Termination reason: Refutation
% 0.16/0.52 % (3868210)Time elapsed: 0.058 s
% 0.16/0.52 % (3868210)Peak memory usage: 14 MB
% 0.16/0.52 % (3868210)Instructions burned: 107 (million)
% 0.16/0.52 % (3868201)Success in time 0.098 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------