%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM551+1 : 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 : n017.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 3.35s 1.36s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 73 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 35 ~; 29 |; 14 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 28 ( 22 !; 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(f66,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
xQ != slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2313) ).
fof(f68,conjecture,
? [X0] :
( aElement0(X0)
& aElementOf0(X0,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f69,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& aElementOf0(X0,xQ) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f75,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f82,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f125,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f126,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK1(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f127]) ).
fof(f150,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f151,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f67]) ).
fof(f152,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f165,plain,
! [X0] :
( aElementOf0(sK1(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f128]) ).
fof(f190,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f240,plain,
( ~ aSet0(xQ)
| slcrc0 = xQ
| ~ aElement0(sK1(xQ)) ),
inference(resolution,[],[f165,f152]) ).
fof(f242,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 = X0
| aElement0(sK1(X0))
| ~ aSet0(X0) ),
inference(resolution,[],[f165,f190]) ).
fof(f243,plain,
! [X0] :
( aElement0(sK1(X0))
| slcrc0 = X0
| ~ aSet0(X0) ),
inference(duplicate_literal_removal,[],[f242]) ).
fof(f244,plain,
( slcrc0 = xQ
| ~ aElement0(sK1(xQ)) ),
inference(forward_subsumption_resolution,[],[f240,f150]) ).
fof(f245,plain,
~ aElement0(sK1(xQ)),
inference(forward_subsumption_resolution,[],[f244,f151]) ).
fof(f249,plain,
( slcrc0 = xQ
| ~ aSet0(xQ) ),
inference(resolution,[],[f243,f245]) ).
fof(f250,plain,
~ aSet0(xQ),
inference(forward_subsumption_resolution,[],[f249,f151]) ).
fof(f251,plain,
$false,
inference(forward_subsumption_resolution,[],[f250,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM551+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:22:36 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.35/1.36 % (2913984)Detected formulas, will run a generic FOF schedule.
% 3.35/1.36 % (2913991)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=2239792600:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.36 % (2913993)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=345581336:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.36 % (2913995)dis-21_1_sil=8000:lcm=predicate:random_seed=3777191355: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)
% 3.35/1.36 % (2913992)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3514892202:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.36 % (2913990)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=746342993:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.36 % (2913989)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=4050247373:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.36 % (2913994)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3979249515:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.36 % (2913993)First to succeed.
% 3.35/1.36 % (2913993)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2913984"
% 3.35/1.36 % (2913994)Also succeeded, but the first one will report.
% 3.35/1.36 % (2913992)Also succeeded, but the first one will report.
% 3.35/1.36 % (2913995)Instruction limit reached!
% 3.35/1.36 % (2913995)------------------------------
% 3.35/1.36 % (2913995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.36 % (2913995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.36 % (2913995)CaDiCaL version: 2.1.3
% 3.35/1.36 % (2913995)Termination reason: Instruction limit
% 3.35/1.36 % (2913995)Termination phase: Saturation
% 3.35/1.36 % (2913995)Time elapsed: 0.058 s
% 3.35/1.36 % (2913995)Peak memory usage: 88 MB
% 3.35/1.36 % (2913995)Instructions burned: 130 (million)
% 3.35/1.36 % (2914003)lrs+10_1_sil=8000:sp=occurrence:random_seed=3205725028:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.35/1.36 % (2914003)Also succeeded, but the first one will report.
% 3.35/1.36 % (2913993)Refutation found. Thanks to Tanya!
% 3.35/1.36 % SZS status Theorem for theBenchmark
% 3.35/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.36 % (2913993)------------------------------
% 3.35/1.36 % (2913993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.36 % (2913993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.36 % (2913993)CaDiCaL version: 2.1.3
% 3.35/1.36 % (2913993)Termination reason: Refutation
% 3.35/1.36 % (2913993)Time elapsed: 0.004 s
% 3.35/1.36 % (2913993)Peak memory usage: 88 MB
% 3.35/1.36 % (2913993)Instructions burned: 4 (million)
% 3.35/1.36 % (2913993)------------------------------
% 3.35/1.36 % (2913993)------------------------------
% 3.35/1.36 % (2913984)Success in time 0.408 s
% 3.35/1.36 % Vampire exiting
%------------------------------------------------------------------------------