%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS216+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 11:41:54 AM UTC 2026
% Result : Theorem 2.77s 1.35s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 18 unt; 4 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 192 ( 91 ~; 72 |; 18 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 101 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ! [X2] :
( model(X2,X0)
=> model(X2,X1) )
<=> status(X0,X1,thm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
fof(f18,axiom,
! [X0,X1] :
( ( ! [X2] : model(X2,X0)
& ! [X3] : model(X3,not(X1)) )
<=> status(X0,X1,uns) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uns) ).
fof(f22,axiom,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& ~ status(X2,X3,X1) )
<=> nota(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nota) ).
fof(f26,axiom,
! [X0,X1] :
( model(X0,X1)
<=> ~ model(X0,not(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not) ).
fof(f27,axiom,
? [X0] :
! [X1] : model(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tautology) ).
fof(f29,axiom,
? [X0] :
! [X1] : ~ model(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contradiction) ).
fof(f33,conjecture,
nota(uns,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nota_uns_thm) ).
fof(f34,negated_conjecture,
~ nota(uns,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ nota(uns,thm),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& ~ status(X2,X3,X1) )
=> nota(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f37,plain,
! [X0,X1] :
( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
<=> status(X0,X1,thm) ),
inference(ennf_transformation,[],[f5]) ).
fof(f38,plain,
! [X0,X1] :
( nota(X0,X1)
| ! [X2,X3] :
( ~ status(X2,X3,X0)
| status(X2,X3,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( ( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
| ~ status(X0,X1,thm) )
& ( status(X0,X1,thm)
| ? [X2] :
( ~ model(X2,X1)
& model(X2,X0) ) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
| ~ status(X0,X1,thm) )
& ( status(X0,X1,thm)
| ? [X3] :
( ~ model(X3,X1)
& model(X3,X0) ) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
| ~ status(X0,X1,thm) )
& ( status(X0,X1,thm)
| ( ~ model(sK0(X0,X1),X1)
& model(sK0(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( ( ! [X2] : model(X2,X0)
& ! [X3] : model(X3,not(X1)) )
| ~ status(X0,X1,uns) )
& ( status(X0,X1,uns)
| ? [X2] : ~ model(X2,X0)
| ? [X3] : ~ model(X3,not(X1)) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( ! [X2] : model(X2,X0)
& ! [X3] : model(X3,not(X1)) )
| ~ status(X0,X1,uns) )
& ( status(X0,X1,uns)
| ? [X2] : ~ model(X2,X0)
| ? [X3] : ~ model(X3,not(X1)) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( ! [X2] : model(X2,X0)
& ! [X3] : model(X3,not(X1)) )
| ~ status(X0,X1,uns) )
& ( status(X0,X1,uns)
| ? [X4] : ~ model(X4,X0)
| ? [X5] : ~ model(X5,not(X1)) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ! [X2] : model(X2,X0)
& ! [X3] : model(X3,not(X1)) )
| ~ status(X0,X1,uns) )
& ( status(X0,X1,uns)
| ~ model(sK1(X0),X0)
| ~ model(sK2(X1),not(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X4,sK1(X0)),skolemize(X5,sK2(X1))],[f45]) ).
fof(f50,plain,
! [X1] : ~ model(X1,sK16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f29]) ).
fof(f52,plain,
! [X1] : model(X1,sK20),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f27]) ).
fof(f53,plain,
! [X0,X1] :
( ( model(X0,X1)
| model(X0,not(X1)) )
& ( ~ model(X0,not(X1))
| ~ model(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f62,plain,
~ nota(uns,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ status(X0,X1,thm)
| ~ model(X2,X0)
| model(X2,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( nota(X0,X1)
| ~ status(X2,X3,X0)
| status(X2,X3,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
! [X0,X1] :
( status(X0,X1,uns)
| ~ model(sK1(X0),X0)
| ~ model(sK2(X1),not(X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f68,plain,
! [X3,X0,X1] :
( ~ status(X0,X1,uns)
| model(X3,not(X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f81,plain,
! [X1] : ~ model(X1,sK16),
inference(cnf_transformation,[],[f50]) ).
fof(f84,plain,
! [X1] : model(X1,sK20),
inference(cnf_transformation,[],[f52]) ).
fof(f85,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f86,plain,
! [X0,X1] :
( model(X0,not(X1))
| model(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f108,plain,
! [X0,X1] :
( ~ status(X0,X1,uns)
| status(X0,X1,thm) ),
inference(resolution,[],[f66,f62]) ).
fof(f267,plain,
! [X0,X1] :
( status(X0,X1,thm)
| ~ model(sK2(X1),not(X1))
| ~ model(sK1(X0),X0) ),
inference(resolution,[],[f67,f108]) ).
fof(f268,plain,
! [X2,X0,X1] :
( ~ model(sK1(X0),X0)
| ~ model(sK2(X1),not(X1))
| model(X2,not(X1)) ),
inference(resolution,[],[f67,f68]) ).
fof(f271,definition,
( spl24_25
<=> ! [X1] : ~ model(sK2(X1),not(X1)) ),
introduced(definition,[new_symbols(definition,[spl24_25])],[avatar_definition]) ).
fof(f272,plain,
( ! [X1] : ~ model(sK2(X1),not(X1))
| ~ spl24_25 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f278,definition,
( spl24_27
<=> ! [X2,X1] :
( ~ model(sK2(X1),not(X1))
| model(X2,not(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl24_27])],[avatar_definition]) ).
fof(f279,plain,
( ! [X2,X1] :
( model(X2,not(X1))
| ~ model(sK2(X1),not(X1)) )
| ~ spl24_27 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f281,definition,
( spl24_28
<=> ! [X0] : ~ model(sK1(X0),X0) ),
introduced(definition,[new_symbols(definition,[spl24_28])],[avatar_definition]) ).
fof(f282,plain,
( ! [X0] : ~ model(sK1(X0),X0)
| ~ spl24_28 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f283,plain,
( spl24_27
| spl24_28 ),
inference(avatar_split_clause,[],[f268,f281,f278]) ).
fof(f285,plain,
( ! [X0] : model(sK2(X0),X0)
| ~ spl24_25 ),
inference(resolution,[],[f272,f86]) ).
fof(f287,plain,
( $false
| ~ spl24_25 ),
inference(resolution,[],[f285,f81]) ).
fof(f289,plain,
~ spl24_25,
inference(avatar_contradiction_clause,[],[f287]) ).
fof(f306,plain,
( ! [X0,X1] :
( ~ model(sK2(X0),not(X0))
| ~ model(X1,X0) )
| ~ spl24_27 ),
inference(resolution,[],[f279,f85]) ).
fof(f351,plain,
! [X2,X0,X1] :
( model(X2,X0)
| ~ model(sK1(X1),X1)
| ~ model(X2,X1)
| ~ model(sK2(X0),not(X0)) ),
inference(resolution,[],[f267,f65]) ).
fof(f802,definition,
( spl24_93
<=> ! [X0,X1] :
( ~ model(sK1(X0),X0)
| ~ model(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl24_93])],[avatar_definition]) ).
fof(f803,plain,
( ! [X0,X1] :
( ~ model(sK1(X0),X0)
| ~ model(X1,X0) )
| ~ spl24_93 ),
inference(avatar_component_clause,[],[f802]) ).
fof(f1018,plain,
( $false
| ~ spl24_28 ),
inference(resolution,[],[f282,f84]) ).
fof(f1019,plain,
~ spl24_28,
inference(avatar_contradiction_clause,[],[f1018]) ).
fof(f1064,plain,
( ! [X2,X0,X1] :
( ~ model(sK2(X1),not(X1))
| ~ model(sK1(X2),X2)
| ~ model(X0,X2)
| ~ model(sK2(X1),not(X1)) )
| ~ spl24_27 ),
inference(resolution,[],[f306,f351]) ).
fof(f1075,plain,
( ! [X2,X0,X1] :
( ~ model(sK2(X1),not(X1))
| ~ model(sK1(X2),X2)
| ~ model(X0,X2) )
| ~ spl24_27 ),
inference(duplicate_literal_removal,[],[f1064]) ).
fof(f1076,plain,
( spl24_93
| spl24_25
| ~ spl24_27 ),
inference(avatar_split_clause,[],[f1075,f278,f271,f802]) ).
fof(f1367,plain,
( ! [X0] : ~ model(sK1(X0),X0)
| ~ spl24_93 ),
inference(factoring,[],[f803]) ).
fof(f1369,plain,
( spl24_28
| ~ spl24_93 ),
inference(avatar_split_clause,[],[f1367,f802,f281]) ).
cnf(s25,plain,
( spl24_27
| spl24_28 ),
inference(sat_conversion,[],[f283]) ).
cnf(s26,plain,
~ spl24_25,
inference(sat_conversion,[],[f289]) ).
cnf(s140,plain,
~ spl24_28,
inference(sat_conversion,[],[f1019]) ).
cnf(s165,plain,
( spl24_25
| ~ spl24_27
| spl24_93 ),
inference(sat_conversion,[],[f1076]) ).
cnf(s217,plain,
( spl24_28
| ~ spl24_93 ),
inference(sat_conversion,[],[f1369]) ).
cnf(s223,plain,
~ spl24_93,
inference(rat,[],[s217,s140]) ).
cnf(s232,plain,
~ spl24_27,
inference(rat,[],[s165,s223,s26]) ).
cnf(s233,plain,
$false,
inference(rat,[],[s25,s140,s232]) ).
fof(f1375,plain,
$false,
inference(avatar_sat_refutation,[],[s233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS216+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.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 13:40:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.77/1.35 % (2045593)Detected formulas, will run a generic FOF schedule.
% 2.77/1.35 % (2045604)dis-21_1_sil=8000:lcm=predicate:random_seed=241287993: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)
% 2.77/1.35 % (2045604)First to succeed.
% 2.77/1.35 % (2045604)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2045593"
% 2.77/1.35 % (2045598)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=2839592413:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.35 % (2045601)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1398318646:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.35 % (2045602)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4199059969:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.35 % (2045599)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=3486610684:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.35 % (2045600)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=1266779090:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.35 % (2045603)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3650280583:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.35 % (2045601)Refutation not found, incomplete strategy
% 2.77/1.35 % (2045601)------------------------------
% 2.77/1.35 % (2045601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.35 % (2045601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.35 % (2045601)CaDiCaL version: 2.1.3
% 2.77/1.35 % (2045601)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.35 % (2045601)Time elapsed: 0.001 s
% 2.77/1.35 % (2045601)Peak memory usage: 88 MB
% 2.77/1.35 % (2045602)Also succeeded, but the first one will report.
% 2.77/1.35 % (2045603)Also succeeded, but the first one will report.
% 2.77/1.35 % (2045604)Refutation found. Thanks to Tanya!
% 2.77/1.35 % SZS status Theorem for theBenchmark
% 2.77/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.35 % (2045604)------------------------------
% 2.77/1.35 % (2045604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.35 % (2045604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.35 % (2045604)CaDiCaL version: 2.1.3
% 2.77/1.35 % (2045604)Termination reason: Refutation
% 2.77/1.35 % (2045604)Time elapsed: 0.010 s
% 2.77/1.35 % (2045604)Peak memory usage: 90 MB
% 2.77/1.35 % (2045604)Instructions burned: 25 (million)
% 2.77/1.35 % (2045604)------------------------------
% 2.77/1.35 % (2045604)------------------------------
% 2.77/1.35 % (2045593)Success in time 0.309 s
% 2.77/1.35 % Vampire exiting
%------------------------------------------------------------------------------