%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM533+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:15:37 PM UTC 2026
% Result : Theorem 3.42s 1.45s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 81 ( 23 ~; 13 |; 33 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,conjecture,
( ( ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,xB) )
& aSubsetOf0(xA,xB)
& ! [X0] :
( aElementOf0(X0,xB)
=> aElementOf0(X0,xC) )
& aSubsetOf0(xB,xC) )
=> ( ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,xC) )
| aSubsetOf0(xA,xC) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f16,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,xB) )
& aSubsetOf0(xA,xB)
& ! [X0] :
( aElementOf0(X0,xB)
=> aElementOf0(X0,xC) )
& aSubsetOf0(xB,xC) )
=> ( ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,xC) )
| aSubsetOf0(xA,xC) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f21,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,xB) )
& aSubsetOf0(xA,xB)
& ! [X1] :
( aElementOf0(X1,xB)
=> aElementOf0(X1,xC) )
& aSubsetOf0(xB,xC) )
=> ( ! [X2] :
( aElementOf0(X2,xA)
=> aElementOf0(X2,xC) )
| aSubsetOf0(xA,xC) ) ),
inference(rectify,[],[f16]) ).
fof(f32,plain,
( ? [X2] :
( ~ aElementOf0(X2,xC)
& aElementOf0(X2,xA) )
& ~ aSubsetOf0(xA,xC)
& ! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xA) )
& aSubsetOf0(xA,xB)
& ! [X1] :
( aElementOf0(X1,xC)
| ~ aElementOf0(X1,xB) )
& aSubsetOf0(xB,xC) ),
inference(ennf_transformation,[],[f21]) ).
fof(f33,plain,
( ? [X2] :
( ~ aElementOf0(X2,xC)
& aElementOf0(X2,xA) )
& ~ aSubsetOf0(xA,xC)
& ! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xA) )
& aSubsetOf0(xA,xB)
& ! [X1] :
( aElementOf0(X1,xC)
| ~ aElementOf0(X1,xB) )
& aSubsetOf0(xB,xC) ),
inference(flattening,[],[f32]) ).
fof(f42,plain,
( ? [X0] :
( ~ aElementOf0(X0,xC)
& aElementOf0(X0,xA) )
& ~ aSubsetOf0(xA,xC)
& ! [X1] :
( aElementOf0(X1,xB)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,xB)
& ! [X2] :
( aElementOf0(X2,xC)
| ~ aElementOf0(X2,xB) )
& aSubsetOf0(xB,xC) ),
inference(rectify,[],[f33]) ).
fof(f43,plain,
( ~ aElementOf0(sK2,xC)
& aElementOf0(sK2,xA)
& ~ aSubsetOf0(xA,xC)
& ! [X1] :
( aElementOf0(X1,xB)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,xB)
& ! [X2] :
( aElementOf0(X2,xC)
| ~ aElementOf0(X2,xB) )
& aSubsetOf0(xB,xC) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f42]) ).
fof(f59,plain,
! [X2] :
( aElementOf0(X2,xC)
| ~ aElementOf0(X2,xB) ),
inference(cnf_transformation,[],[f43]) ).
fof(f61,plain,
! [X1] :
( aElementOf0(X1,xB)
| ~ aElementOf0(X1,xA) ),
inference(cnf_transformation,[],[f43]) ).
fof(f63,plain,
aElementOf0(sK2,xA),
inference(cnf_transformation,[],[f43]) ).
fof(f64,plain,
~ aElementOf0(sK2,xC),
inference(cnf_transformation,[],[f43]) ).
fof(f72,plain,
~ aElementOf0(sK2,xB),
inference(resolution,[],[f59,f64]) ).
fof(f73,plain,
~ aElementOf0(sK2,xA),
inference(resolution,[],[f61,f72]) ).
fof(f74,plain,
$false,
inference(resolution,[],[f73,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM533+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:22:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/1.45 % (3379989)Detected formulas, will run a generic FOF schedule.
% 3.42/1.45 % (3379996)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=559354297:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.42/1.45 % (3380000)dis-21_1_sil=8000:lcm=predicate:random_seed=1483106172: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)
% 3.42/1.45 % (3380000)First to succeed.
% 3.42/1.45 % (3380000)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3379989"
% 3.42/1.45 % (3379998)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3049391946:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.42/1.45 % (3379994)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=62018370:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.42/1.45 % (3379997)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=383639301:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.42/1.45 % (3379995)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=2752347479:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.42/1.45 % (3379998)Also succeeded, but the first one will report.
% 3.42/1.45 % (3379997)Also succeeded, but the first one will report.
% 3.42/1.45 % (3379999)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3583250117:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.42/1.45 % (3379999)Also succeeded, but the first one will report.
% 3.42/1.45 % (3380000)Refutation found. Thanks to Tanya!
% 3.42/1.45 % SZS status Theorem for theBenchmark
% 3.42/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.45 % (3380000)------------------------------
% 3.42/1.45 % (3380000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.45 % (3380000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.45 % (3380000)CaDiCaL version: 2.1.3
% 3.42/1.45 % (3380000)Termination reason: Refutation
% 3.42/1.45 % (3380000)Time elapsed: 0.002 s
% 3.42/1.45 % (3380000)Peak memory usage: 88 MB
% 3.42/1.45 % (3380000)Instructions burned: 1 (million)
% 3.42/1.45 % (3380000)------------------------------
% 3.42/1.45 % (3380000)------------------------------
% 3.42/1.45 % (3379989)Success in time 0.402 s
% 3.42/1.45 % Vampire exiting
%------------------------------------------------------------------------------