%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM564+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 : n012.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 12:24:49 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 28 unt; 3 def)
% Number of atoms : 187 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 183 ( 72 ~; 77 |; 15 &)
% ( 15 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 55 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
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(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
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(f75,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f76,axiom,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(f78,axiom,
xK = sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f79,conjecture,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f80,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(negated_conjecture,[status(cth)],[f79]) ).
fof(f81,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(flattening,[],[f80]) ).
fof(f87,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f142,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f166,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(f167,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,[],[f166]) ).
fof(f195,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f87]) ).
fof(f196,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f87]) ).
fof(f201,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK1(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f204,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aSet0(X1)
| ~ aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f234,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f235,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f255,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sz00 = sbrdtbr0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f290,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,[],[f167]) ).
fof(f335,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f337,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f76]) ).
fof(f343,plain,
sz00 = xK,
inference(cnf_transformation,[],[f78]) ).
fof(f344,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[],[f81]) ).
fof(f345,plain,
aElementOf0(xK,szNzAzT0),
inference(definition_unfolding,[],[f235,f343]) ).
fof(f352,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sbrdtbr0(X0) = xK ),
inference(definition_unfolding,[],[f255,f343]) ).
fof(f356,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(definition_unfolding,[],[f344,f343]) ).
fof(f357,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f196]) ).
fof(f358,plain,
! [X1] : ~ aElementOf0(X1,slcrc0),
inference(equality_resolution,[],[f195]) ).
fof(f372,plain,
( ~ aSet0(slcrc0)
| xK = sbrdtbr0(slcrc0) ),
inference(equality_resolution,[],[f352]) ).
fof(f383,plain,
! [X2,X3,X0] :
( ~ aElementOf0(sbrdtbr0(X3),szNzAzT0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| slbdtsldtrb0(X0,sbrdtbr0(X3)) != X2 ),
inference(equality_resolution,[],[f290]) ).
fof(f384,plain,
! [X3,X0] :
( ~ aElementOf0(sbrdtbr0(X3),szNzAzT0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,slbdtsldtrb0(X0,sbrdtbr0(X3))) ),
inference(equality_resolution,[],[f383]) ).
fof(f404,plain,
~ aSet0(slcrc0),
inference(consistent_polarity_flipping,[],[f357]) ).
fof(f405,plain,
! [X1] : aElementOf0(X1,slcrc0),
inference(consistent_polarity_flipping,[],[f358]) ).
fof(f409,plain,
! [X0,X1] :
( ~ aSet0(X1)
| aSet0(X0)
| ~ aSubsetOf0(X1,X0) ),
inference(consistent_polarity_flipping,[],[f204]) ).
fof(f412,plain,
! [X0,X1] :
( ~ aElementOf0(sK1(X0,X1),X1)
| aSet0(X0)
| aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(consistent_polarity_flipping,[],[f201]) ).
fof(f441,plain,
~ aSet0(szNzAzT0),
inference(consistent_polarity_flipping,[],[f234]) ).
fof(f442,plain,
~ aElementOf0(xK,szNzAzT0),
inference(consistent_polarity_flipping,[],[f345]) ).
fof(f463,plain,
( aSet0(slcrc0)
| xK = sbrdtbr0(slcrc0) ),
inference(consistent_polarity_flipping,[],[f372]) ).
fof(f498,plain,
! [X3,X0] :
( ~ aElementOf0(X3,slbdtsldtrb0(X0,sbrdtbr0(X3)))
| aSet0(X0)
| ~ aSubsetOf0(X3,X0)
| aElementOf0(sbrdtbr0(X3),szNzAzT0) ),
inference(consistent_polarity_flipping,[],[f384]) ).
fof(f538,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(consistent_polarity_flipping,[],[f356]) ).
fof(f542,definition,
( spl21_1
<=> xK = sbrdtbr0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f544,plain,
( xK = sbrdtbr0(slcrc0)
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f546,definition,
( spl21_2
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f547,plain,
( ~ aSet0(slcrc0)
| spl21_2 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f549,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f463,f546,f542]) ).
fof(f555,plain,
~ spl21_2,
inference(avatar_split_clause,[],[f404,f546]) ).
fof(f558,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(superposition,[],[f538,f337]) ).
fof(f567,definition,
( spl21_5
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f568,plain,
( ~ aSet0(xS)
| spl21_5 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f569,plain,
( aSet0(xS)
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f574,plain,
( ! [X0] :
( ~ aSubsetOf0(xS,X0)
| aSet0(X0) )
| ~ spl21_5 ),
inference(resolution,[],[f409,f569]) ).
fof(f575,plain,
( aSet0(szNzAzT0)
| ~ spl21_5 ),
inference(resolution,[],[f574,f335]) ).
fof(f578,plain,
( $false
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f575,f441]) ).
fof(f579,plain,
~ spl21_5,
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f748,plain,
! [X0] :
( aSet0(X0)
| aSet0(slcrc0)
| aSubsetOf0(slcrc0,X0) ),
inference(resolution,[],[f412,f405]) ).
fof(f761,plain,
( ! [X0] :
( aSubsetOf0(slcrc0,X0)
| aSet0(X0) )
| spl21_2 ),
inference(forward_subsumption_resolution,[],[f748,f547]) ).
fof(f1076,plain,
( ! [X0] :
( ~ aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| aSet0(X0)
| ~ aSubsetOf0(slcrc0,X0)
| aElementOf0(xK,szNzAzT0) )
| ~ spl21_1 ),
inference(superposition,[],[f498,f544]) ).
fof(f1081,plain,
( ! [X0] :
( ~ aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| aSet0(X0)
| aElementOf0(xK,szNzAzT0) )
| ~ spl21_1
| spl21_2 ),
inference(forward_subsumption_resolution,[],[f1076,f761]) ).
fof(f1085,plain,
( ! [X0] :
( ~ aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| aSet0(X0) )
| ~ spl21_1
| spl21_2 ),
inference(forward_subsumption_resolution,[],[f1081,f442]) ).
fof(f1682,plain,
( ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| aSet0(xS)
| ~ spl21_1
| spl21_2 ),
inference(superposition,[],[f1085,f337]) ).
fof(f1685,plain,
( aSet0(xS)
| ~ spl21_1
| spl21_2 ),
inference(forward_subsumption_resolution,[],[f1682,f558]) ).
fof(f1696,plain,
( $false
| ~ spl21_1
| spl21_2
| spl21_5 ),
inference(forward_subsumption_resolution,[],[f1685,f568]) ).
fof(f1697,plain,
( ~ spl21_1
| spl21_2
| spl21_5 ),
inference(avatar_contradiction_clause,[],[f1696]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f549]) ).
cnf(s3,plain,
~ spl21_2,
inference(sat_conversion,[],[f555]) ).
cnf(s5,plain,
~ spl21_5,
inference(sat_conversion,[],[f579]) ).
cnf(s61,plain,
( ~ spl21_1
| spl21_2
| spl21_5 ),
inference(sat_conversion,[],[f1697]) ).
cnf(s67,plain,
~ spl21_1,
inference(rat,[],[s61,s5,s3]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s1,s3,s67]) ).
fof(f1698,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM564+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 20:30:19 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.32 Running first-order model finding
% 0.08/0.32 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
% 0.08/0.38 % (2710357)Will run a generic schedule for satisfiability detection.
% 0.08/0.38 % (2710363)% WARNING: option uhcvi not known.
% 0.08/0.38 % (2710365)dis+10_1_sil=32000:sp=arity:random_seed=3508670914:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.38 % (2710364)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2193785013:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.38 % (2710368)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3367403513:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.38 % (2710362)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1627610900_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.38 % (2710363)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3128263999:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.38 % (2710366)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=672775283:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.38 % (2710367)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3980725388:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.38 % TRYING [1]
% 0.08/0.38 % TRYING [2]
% 0.08/0.38 % TRYING [3]
% 0.08/0.38 % (2710363) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2710357-2710363"...
% 0.08/0.38 % (2710365) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2710357-2710365"...
% 0.08/0.38 % (2710363)...printing done.
% 0.08/0.38 % (2710365)...printing done.
% 0.08/0.38 % TRYING [4]
% 0.08/0.38 % (2710363)Refutation found. Thanks to Tanya!
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.38 % (2710363)------------------------------
% 0.08/0.38 % (2710363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.38 % (2710363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.38 % (2710363)CaDiCaL version: 2.1.3
% 0.08/0.38 % (2710363)Termination reason: Refutation
% 0.08/0.38 % (2710363)Time elapsed: 0.022 s
% 0.08/0.38 % (2710363)Peak memory usage: 13 MB
% 0.08/0.38 % (2710363)Instructions burned: 53 (million)
% 0.08/0.38 % (2710357)Success in time 0.048 s
% 0.08/0.38 % Vampire exiting
%------------------------------------------------------------------------------