%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM550+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:24:46 PM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 10 unt; 2 def)
% Number of atoms : 100 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 42 ~; 29 |; 25 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 21 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f65,axiom,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f67,conjecture,
~ ( ~ ? [X0] : aElementOf0(X0,xQ)
& xQ = slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f68,negated_conjecture,
~ ~ ( ~ ? [X0] : aElementOf0(X0,xQ)
& xQ = slcrc0 ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f76,plain,
( ~ ? [X0] : aElementOf0(X0,xQ)
& xQ = slcrc0 ),
inference(flattening,[],[f68]) ).
fof(f79,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f127,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f161,plain,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f65]) ).
fof(f162,plain,
( ! [X0] : ~ aElementOf0(X0,xQ)
& xQ = slcrc0 ),
inference(ennf_transformation,[],[f76]) ).
fof(f169,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f170,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f169]) ).
fof(f171,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f170]) ).
fof(f172,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK4(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f171]) ).
fof(f192,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f127]) ).
fof(f218,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f172]) ).
fof(f283,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f326,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
fof(f358,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f161]) ).
fof(f365,plain,
slcrc0 = xQ,
inference(cnf_transformation,[],[f162]) ).
fof(f368,plain,
! [X0] :
( aSet0(X0)
| xQ != X0 ),
inference(definition_unfolding,[],[f218,f365]) ).
fof(f372,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| xQ != X0
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f283,f365]) ).
fof(f386,plain,
aSet0(xQ),
inference(equality_resolution,[],[f368]) ).
fof(f393,plain,
( sz00 = sbrdtbr0(xQ)
| ~ aSet0(xQ) ),
inference(equality_resolution,[],[f372]) ).
fof(f410,definition,
( spl19_1
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f414,definition,
( spl19_2
<=> sz00 = sbrdtbr0(xQ) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f416,plain,
( sz00 = sbrdtbr0(xQ)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f417,plain,
( ~ spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f393,f414,f410]) ).
fof(f423,plain,
spl19_1,
inference(avatar_split_clause,[],[f386,f410]) ).
fof(f437,plain,
( sz00 = xk
| ~ spl19_2 ),
inference(forward_demodulation,[],[f358,f416]) ).
fof(f438,plain,
( $false
| ~ spl19_2 ),
inference(forward_subsumption_resolution,[],[f437,f326]) ).
fof(f439,plain,
~ spl19_2,
inference(avatar_contradiction_clause,[],[f438]) ).
cnf(s1,plain,
( ~ spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f417]) ).
cnf(s3,plain,
spl19_1,
inference(sat_conversion,[],[f423]) ).
cnf(s4,plain,
~ spl19_2,
inference(sat_conversion,[],[f439]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f440,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM550+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 20:27:30 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.48 % (2372321)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (2372326)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2732688698_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (2372327)% WARNING: option uhcvi not known.
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % (2372327)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1978889569:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (2372328)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1292622229:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (2372331)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1732187293:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (2372329)dis+10_1_sil=32000:sp=arity:random_seed=1619385955:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (2372330)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=974115960:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (2372332)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2383685903:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % TRYING [3]
% 0.15/0.48 % TRYING [4]
% 0.15/0.48 % (2372329) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2372321-2372329"...
% 0.15/0.48 % (2372327) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2372321-2372327"...
% 0.15/0.48 % (2372327)...printing done.
% 0.15/0.48 % (2372329)...printing done.
% 0.15/0.48 % (2372330) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2372321-2372330"...
% 0.15/0.48 % (2372332) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2372321-2372332"...
% 0.15/0.48 % (2372328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2372321-2372328"...
% 0.15/0.48 % (2372329)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (2372329)------------------------------
% 0.15/0.48 % (2372329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (2372329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (2372329)CaDiCaL version: 2.1.3
% 0.15/0.48 % (2372329)Termination reason: Refutation
% 0.15/0.48 % (2372329)Time elapsed: 0.007 s
% 0.15/0.48 % (2372329)Peak memory usage: 13 MB
% 0.15/0.48 % (2372329)Instructions burned: 9 (million)
% 0.15/0.48 % (2372321)Success in time 0.052 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------