%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM557+3 : 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 12:15:44 PM UTC 2026
% Result : Theorem 0.17s 1.13s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 8 unt; 2 def)
% Number of atoms : 46 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 43 ( 16 ~; 10 |; 12 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 4 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f72,axiom,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) )
& aSubsetOf0(xP,xS)
& sbrdtbr0(xP) = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2431) ).
fof(f73,conjecture,
( ( ( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk )
| aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f74,negated_conjecture,
~ ( ( ( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk )
| aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(negated_conjecture,[status(cth)],[f73]) ).
fof(f168,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xP) )
& aSubsetOf0(xP,xS)
& sbrdtbr0(xP) = xk ),
inference(ennf_transformation,[],[f72]) ).
fof(f169,plain,
( ( ( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,xP) )
& ~ aSubsetOf0(xP,xS) )
| xk != sbrdtbr0(xP) )
& ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f74]) ).
fof(f227,plain,
( ( ( ~ aElementOf0(sK19,xS)
& aElementOf0(sK19,xP)
& ~ aSubsetOf0(xP,xS) )
| xk != sbrdtbr0(xP) )
& ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f169]) ).
fof(f398,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f168]) ).
fof(f399,plain,
aSubsetOf0(xP,xS),
inference(cnf_transformation,[],[f168]) ).
fof(f402,plain,
( ~ aSubsetOf0(xP,xS)
| xk != sbrdtbr0(xP) ),
inference(cnf_transformation,[],[f227]) ).
fof(f432,definition,
( spl20_1
<=> xk = sbrdtbr0(xP) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f436,definition,
( spl20_2
<=> aSubsetOf0(xP,xS) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f439,plain,
( ~ spl20_1
| ~ spl20_2 ),
inference(avatar_split_clause,[],[f402,f436,f432]) ).
fof(f450,plain,
spl20_1,
inference(avatar_split_clause,[],[f398,f432]) ).
fof(f451,plain,
spl20_2,
inference(avatar_split_clause,[],[f399,f436]) ).
cnf(s1,plain,
( ~ spl20_1
| ~ spl20_2 ),
inference(sat_conversion,[],[f439]) ).
cnf(s4,plain,
spl20_1,
inference(sat_conversion,[],[f450]) ).
cnf(s5,plain,
spl20_2,
inference(sat_conversion,[],[f451]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s5,s4]) ).
fof(f476,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM557+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:29:03 UTC 2026
% 0.11/0.38 % 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
% 0.17/1.13 % (3383203)Detected formulas, will run a generic FOF schedule.
% 0.17/1.13 % (3383213)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=525322753:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.13 % (3383211)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3916463733:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.13 % (3383214)dis-21_1_sil=8000:lcm=predicate:random_seed=22130759: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)
% 0.17/1.13 % (3383212)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2854901699:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.13 % (3383209)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=1352367527:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.13 % (3383208)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=2841695827:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.13 % (3383210)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=172762773:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.13 % (3383213)First to succeed.
% 0.17/1.13 % (3383213)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3383203"
% 0.17/1.13 % (3383212)Also succeeded, but the first one will report.
% 0.17/1.13 % (3383214)Also succeeded, but the first one will report.
% 0.17/1.13 % (3383211)Also succeeded, but the first one will report.
% 0.17/1.13 % (3383213)Refutation found. Thanks to Tanya!
% 0.17/1.13 % SZS status Theorem for theBenchmark
% 0.17/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.13 % (3383213)------------------------------
% 0.17/1.13 % (3383213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.13 % (3383213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.13 % (3383213)CaDiCaL version: 2.1.3
% 0.17/1.13 % (3383213)Termination reason: Refutation
% 0.17/1.13 % (3383213)Time elapsed: 0.003 s
% 0.17/1.13 % (3383213)Peak memory usage: 89 MB
% 0.17/1.13 % (3383213)Instructions burned: 7 (million)
% 0.17/1.13 % (3383213)------------------------------
% 0.17/1.13 % (3383213)------------------------------
% 0.17/1.13 % (3383203)Success in time 0.326 s
% 0.17/1.13 % Vampire exiting
%------------------------------------------------------------------------------