%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM548+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 : n005.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 0.32s 0.47s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 19 unt; 1 def)
% Number of atoms : 219 ( 38 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 274 ( 107 ~; 104 |; 48 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 66 !; 6 ?)
% 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(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
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(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(f65,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(f66,conjecture,
isFinite0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f67,negated_conjecture,
~ isFinite0(xQ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f74,plain,
~ isFinite0(xQ),
inference(flattening,[],[f67]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f124,plain,
! [X0] :
( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f149,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(f150,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,[],[f149]) ).
fof(f167,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f82]) ).
fof(f168,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f168]) ).
fof(f170,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f169]) ).
fof(f185,plain,
! [X0] :
( ( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0) )
& ( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f124]) ).
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(nnf_transformation,[],[f150]) ).
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)
& ! [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,[],[f204]) ).
fof(f206,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,[],[f205]) ).
fof(f207,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))],[f206]) ).
fof(f216,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f272,plain,
! [X0] :
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f307,plain,
! [X2,X0,X1,X4] :
( sbrdtbr0(X4) = X1
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f308,plain,
! [X2,X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f317,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f320,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f324,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f65]) ).
fof(f325,plain,
~ isFinite0(xQ),
inference(cnf_transformation,[],[f74]) ).
fof(f346,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f308]) ).
fof(f347,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f307]) ).
fof(f867,plain,
( aSubsetOf0(xQ,xS)
| ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f346,f324]) ).
fof(f872,plain,
( aSubsetOf0(xQ,xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f867,f320]) ).
fof(f873,plain,
aSubsetOf0(xQ,xS),
inference(forward_subsumption_resolution,[],[f872,f317]) ).
fof(f877,plain,
( aSet0(xQ)
| ~ aSet0(xS) ),
inference(resolution,[],[f873,f216]) ).
fof(f878,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f877,f320]) ).
fof(f882,definition,
( spl15_38
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl15_38])],[avatar_definition]) ).
fof(f883,plain,
( aSet0(xQ)
| ~ spl15_38 ),
inference(avatar_component_clause,[],[f882]) ).
fof(f894,plain,
spl15_38,
inference(avatar_split_clause,[],[f878,f882]) ).
fof(f1037,plain,
( xk = sbrdtbr0(xQ)
| ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f347,f324]) ).
fof(f1042,plain,
( xk = sbrdtbr0(xQ)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1037,f320]) ).
fof(f1044,plain,
xk = sbrdtbr0(xQ),
inference(forward_subsumption_resolution,[],[f1042,f317]) ).
fof(f1049,plain,
( ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[],[f272,f1044]) ).
fof(f1051,plain,
( isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[],[f1049,f317]) ).
fof(f1052,plain,
~ aSet0(xQ),
inference(forward_subsumption_resolution,[],[f1051,f325]) ).
fof(f1053,plain,
( $false
| ~ spl15_38 ),
inference(forward_subsumption_resolution,[],[f1052,f883]) ).
fof(f1054,plain,
~ spl15_38,
inference(avatar_contradiction_clause,[],[f1053]) ).
cnf(s38,plain,
spl15_38,
inference(sat_conversion,[],[f894]) ).
cnf(s39,plain,
~ spl15_38,
inference(sat_conversion,[],[f1054]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s38,s39]) ).
fof(f1055,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM548+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 : n005.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 20:26:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.32/0.47 % (139140)Will run a generic schedule for satisfiability detection.
% 0.32/0.47 % (139150)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3781901241:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.32/0.47 % (139146)% WARNING: option uhcvi not known.
% 0.32/0.47 % (139145)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3234962978_2999 on theBenchmark for (2999ds/0Mi)
% 0.32/0.47 % (139147)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2345507358:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.32/0.47 % (139151)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1345964786:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.32/0.47 % (139148)dis+10_1_sil=32000:sp=arity:random_seed=3020730835:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.32/0.47 % (139149)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4101038723:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.32/0.47 % (139146)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=277924939:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.32/0.47 % TRYING [1]
% 0.32/0.47 % TRYING [2]
% 0.32/0.47 % TRYING [3]
% 0.32/0.47 % (139148) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-139140-139148"...
% 0.32/0.47 % (139148)...printing done.
% 0.32/0.47 % (139148)Refutation found. Thanks to Tanya!
% 0.32/0.47 % SZS status Theorem for theBenchmark
% 0.32/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.32/0.47 % (139148)------------------------------
% 0.32/0.47 % (139148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.47 % (139148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.47 % (139148)CaDiCaL version: 2.1.3
% 0.32/0.47 % (139148)Termination reason: Refutation
% 0.32/0.47 % (139148)Time elapsed: 0.018 s
% 0.32/0.47 % (139148)Peak memory usage: 13 MB
% 0.32/0.47 % (139148)Instructions burned: 24 (million)
% 0.32/0.47 % (139140)Success in time 0.053 s
% 0.32/0.47 % Vampire exiting
%------------------------------------------------------------------------------