%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:15:42 PM UTC 2026
% Result : Theorem 2.64s 1.36s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 103 ( 33 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 42 ~; 34 |; 23 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(f67,conjecture,
? [X0] :
( aElement0(X0)
& aElementOf0(X0,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f68,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& aElementOf0(X0,xQ) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f77,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(f78,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f79,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f85,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f128,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f79]) ).
fof(f130,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f131,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK5(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f132]) ).
fof(f146,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
fof(f148,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f178,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f77]) ).
fof(f180,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f77]) ).
fof(f181,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f77]) ).
fof(f185,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f187,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f197,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f133]) ).
fof(f198,plain,
! [X0] :
( aElementOf0(sK5(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f133]) ).
fof(f223,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f237,plain,
( sz00 = sbrdtbr0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f187]) ).
fof(f238,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f197]) ).
fof(f251,plain,
sz00 = sbrdtbr0(slcrc0),
inference(forward_subsumption_resolution,[],[f237,f238]) ).
fof(f260,plain,
! [X0] :
( aElement0(X0)
| ~ aSet0(xS)
| ~ aElementOf0(X0,xQ) ),
inference(resolution,[],[f223,f180]) ).
fof(f271,plain,
! [X0] :
( ~ aSet0(xS)
| ~ aElementOf0(X0,xQ) ),
inference(forward_subsumption_resolution,[],[f260,f185]) ).
fof(f272,plain,
! [X0] : ~ aElementOf0(X0,xQ),
inference(forward_subsumption_resolution,[],[f271,f148]) ).
fof(f300,plain,
( ~ aSet0(xQ)
| slcrc0 = xQ ),
inference(resolution,[],[f198,f272]) ).
fof(f304,plain,
slcrc0 = xQ,
inference(forward_subsumption_resolution,[],[f300,f181]) ).
fof(f320,plain,
sz00 = sbrdtbr0(xQ),
inference(superposition,[],[f251,f304]) ).
fof(f326,plain,
sz00 = xk,
inference(superposition,[],[f178,f320]) ).
fof(f332,plain,
$false,
inference(forward_subsumption_resolution,[],[f326,f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:30:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.64/1.36 % (1987136)Detected formulas, will run a generic FOF schedule.
% 2.64/1.36 % (1987145)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3839037136:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.36 % (1987145)First to succeed.
% 2.64/1.36 % (1987145)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1987136"
% 2.64/1.36 % (1987144)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4005974054:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.36 % (1987142)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=439621840:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.36 % (1987143)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1150802739:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.36 % (1987141)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1491271051:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.36 % (1987146)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=359091768:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.36 % (1987147)dis-21_1_sil=8000:lcm=predicate:random_seed=2470786731:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.64/1.36 % (1987144)Also succeeded, but the first one will report.
% 2.64/1.36 % (1987146)Also succeeded, but the first one will report.
% 2.64/1.36 % (1987147)Instruction limit reached!
% 2.64/1.36 % (1987147)------------------------------
% 2.64/1.36 % (1987147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.36 % (1987147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.36 % (1987147)CaDiCaL version: 2.1.3
% 2.64/1.36 % (1987147)Termination reason: Instruction limit
% 2.64/1.36 % (1987147)Termination phase: Saturation
% 2.64/1.36 % (1987147)Time elapsed: 0.062 s
% 2.64/1.36 % (1987147)Peak memory usage: 88 MB
% 2.64/1.36 % (1987147)Instructions burned: 131 (million)
% 2.64/1.36 % (1987145)Refutation found. Thanks to Tanya!
% 2.64/1.36 % SZS status Theorem for theBenchmark
% 2.64/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.36 % (1987145)------------------------------
% 2.64/1.36 % (1987145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.36 % (1987145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.36 % (1987145)CaDiCaL version: 2.1.3
% 2.64/1.36 % (1987145)Termination reason: Refutation
% 2.64/1.36 % (1987145)Time elapsed: 0.003 s
% 2.64/1.36 % (1987145)Peak memory usage: 88 MB
% 2.64/1.36 % (1987145)Instructions burned: 7 (million)
% 2.64/1.36 % (1987145)------------------------------
% 2.64/1.36 % (1987145)------------------------------
% 2.64/1.36 % (1987136)Success in time 0.297 s
% 2.64/1.36 % Vampire exiting
%------------------------------------------------------------------------------