%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM547+1 : 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 : n010.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 12:24:45 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 15 unt; 1 def)
% Number of atoms : 166 ( 46 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 205 ( 78 ~; 73 |; 44 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 47 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
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/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f63,axiom,
( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f65,conjecture,
? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f66,negated_conjecture,
~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f75,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f147,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(f148,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,[],[f147]) ).
fof(f155,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(ennf_transformation,[],[f66]) ).
fof(f162,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f163,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f162]) ).
fof(f164,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f163]) ).
fof(f165,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))],[f164]) ).
fof(f203,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f204,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f203]) ).
fof(f205,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f204]) ).
fof(f206,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK14(X0,X1,X2),X0)
& sbrdtbr0(sK14(X0,X1,X2)) = X1 )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f205]) ).
fof(f210,plain,
! [X0] :
( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f165]) ).
fof(f309,plain,
! [X2,X0,X1] :
( aSet0(X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f316,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f319,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f320,plain,
slcrc0 != slbdtsldtrb0(xS,xk),
inference(cnf_transformation,[],[f63]) ).
fof(f323,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f155]) ).
fof(f341,plain,
! [X0,X1] :
( aSet0(slbdtsldtrb0(X0,X1))
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f309]) ).
fof(f389,definition,
( spl15_5
<=> aSet0(slbdtsldtrb0(xS,xk)) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f390,plain,
( ~ aSet0(slbdtsldtrb0(xS,xk))
| spl15_5 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f435,plain,
( ~ aSet0(slbdtsldtrb0(xS,xk))
| slcrc0 = slbdtsldtrb0(xS,xk) ),
inference(resolution,[],[f210,f323]) ).
fof(f437,plain,
~ aSet0(slbdtsldtrb0(xS,xk)),
inference(forward_subsumption_resolution,[],[f435,f320]) ).
fof(f445,plain,
~ spl15_5,
inference(avatar_split_clause,[],[f437,f389]) ).
fof(f529,plain,
( ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0)
| spl15_5 ),
inference(resolution,[],[f341,f390]) ).
fof(f530,plain,
( ~ aElementOf0(xk,szNzAzT0)
| spl15_5 ),
inference(forward_subsumption_resolution,[],[f529,f319]) ).
fof(f532,plain,
( $false
| spl15_5 ),
inference(forward_subsumption_resolution,[],[f530,f316]) ).
fof(f533,plain,
spl15_5,
inference(avatar_contradiction_clause,[],[f532]) ).
cnf(s5,plain,
~ spl15_5,
inference(sat_conversion,[],[f445]) ).
cnf(s17,plain,
spl15_5,
inference(sat_conversion,[],[f533]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s5,s17]) ).
fof(f536,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM547+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n010.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 20:27:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.46 % (1286832)Will run a generic schedule for satisfiability detection.
% 0.09/0.46 % (1286837)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2350351478_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.46 % TRYING [1]
% 0.09/0.46 % (1286838)% WARNING: option uhcvi not known.
% 0.09/0.46 % TRYING [2]
% 0.09/0.46 % TRYING [3]
% 0.09/0.46 % (1286839)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2200749829:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.46 % (1286840)dis+10_1_sil=32000:sp=arity:random_seed=3303132251:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.46 % (1286843)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2000591349:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.46 % (1286841)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2905376328:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.46 % (1286842)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=969021697:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.46 % (1286838)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1584399705:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.46 % TRYING [4]
% 0.09/0.46 % (1286840) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1286832-1286840"...
% 0.09/0.46 % (1286838) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1286832-1286838"...
% 0.09/0.46 % (1286840)...printing done.
% 0.09/0.46 % (1286843) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1286832-1286843"...
% 0.09/0.46 % (1286838)...printing done.
% 0.09/0.46 % (1286840)Refutation found. Thanks to Tanya!
% 0.09/0.46 % SZS status Theorem for theBenchmark
% 0.09/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.46 % (1286840)------------------------------
% 0.09/0.46 % (1286840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.46 % (1286840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.46 % (1286840)CaDiCaL version: 2.1.3
% 0.09/0.46 % (1286840)Termination reason: Refutation
% 0.09/0.46 % (1286840)Time elapsed: 0.008 s
% 0.09/0.46 % (1286840)Peak memory usage: 12 MB
% 0.09/0.46 % (1286840)Instructions burned: 10 (million)
% 0.09/0.46 % (1286832)Success in time 0.047 s
% 0.09/0.46 % Vampire exiting
%------------------------------------------------------------------------------