%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS268+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 11:42:00 AM UTC 2026
% Result : Theorem 2.69s 1.27s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 16 unt; 2 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 148 ( 61 ~; 50 |; 28 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 79 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ! [X2] :
( model(X2,X0)
=> model(X2,X1) )
<=> status(X0,X1,thm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
fof(f16,axiom,
! [X0,X1] :
( ( ~ ? [X2] : model(X2,X0)
& ? [X3] : model(X3,X1)
& ? [X4] : ~ model(X4,X1) )
<=> status(X0,X1,wca) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wca) ).
fof(f20,axiom,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& status(X2,X3,X1) )
<=> mighta(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta) ).
fof(f29,axiom,
? [X0] :
! [X1] : ~ model(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contradiction) ).
fof(f32,axiom,
? [X0,X1,X2] :
( model(X0,X1)
& ~ model(X0,X2)
& ? [X3] : model(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_thm_spt) ).
fof(f33,conjecture,
mighta(wca,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta_wca_thm) ).
fof(f34,negated_conjecture,
~ mighta(wca,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ mighta(wca,thm),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& status(X2,X3,X1) )
=> mighta(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f37,plain,
! [X0,X1] :
( mighta(X0,X1)
| ! [X2,X3] :
( ~ status(X2,X3,X0)
| ~ status(X2,X3,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
<=> status(X0,X1,thm) ),
inference(ennf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1] :
( ( ! [X2] : ~ model(X2,X0)
& ? [X3] : model(X3,X1)
& ? [X4] : ~ model(X4,X1) )
<=> status(X0,X1,wca) ),
inference(ennf_transformation,[],[f16]) ).
fof(f41,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,[],[f38]) ).
fof(f42,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,[],[f41]) ).
fof(f43,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))],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( ! [X2] : ~ model(X2,X0)
& ? [X3] : model(X3,X1)
& ? [X4] : ~ model(X4,X1) )
| ~ status(X0,X1,wca) )
& ( status(X0,X1,wca)
| ? [X2] : model(X2,X0)
| ! [X3] : ~ model(X3,X1)
| ! [X4] : model(X4,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( ! [X2] : ~ model(X2,X0)
& ? [X3] : model(X3,X1)
& ? [X4] : ~ model(X4,X1) )
| ~ status(X0,X1,wca) )
& ( status(X0,X1,wca)
| ? [X2] : model(X2,X0)
| ! [X3] : ~ model(X3,X1)
| ! [X4] : model(X4,X1) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ! [X2] : ~ model(X2,X0)
& ? [X3] : model(X3,X1)
& ? [X4] : ~ model(X4,X1) )
| ~ status(X0,X1,wca) )
& ( status(X0,X1,wca)
| ? [X5] : model(X5,X0)
| ! [X6] : ~ model(X6,X1)
| ! [X7] : model(X7,X1) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( ( ! [X2] : ~ model(X2,X0)
& model(sK1(X1),X1)
& ~ model(sK2(X1),X1) )
| ~ status(X0,X1,wca) )
& ( status(X0,X1,wca)
| model(sK3(X0),X0)
| ! [X6] : ~ model(X6,X1)
| ! [X7] : model(X7,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X3,sK1(X1)),skolemize(X4,sK2(X1)),skolemize(X5,sK3(X0))],[f46]) ).
fof(f48,plain,
( model(sK4,sK5)
& ~ model(sK4,sK6)
& model(sK7,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f32]) ).
fof(f51,plain,
! [X1] : ~ model(X1,sK17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f29]) ).
fof(f54,plain,
~ mighta(wca,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( mighta(X0,X1)
| ~ status(X2,X3,X0)
| ~ status(X2,X3,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
! [X0,X1] :
( status(X0,X1,thm)
| model(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X0,X1,X6,X7] :
( status(X0,X1,wca)
| model(sK3(X0),X0)
| ~ model(X6,X1)
| model(X7,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
model(sK7,sK6),
inference(cnf_transformation,[],[f48]) ).
fof(f64,plain,
~ model(sK4,sK6),
inference(cnf_transformation,[],[f48]) ).
fof(f74,plain,
! [X1] : ~ model(X1,sK17),
inference(cnf_transformation,[],[f51]) ).
fof(f88,plain,
! [X0,X1] :
( ~ status(X0,X1,thm)
| ~ status(X0,X1,wca) ),
inference(resolution,[],[f55,f54]) ).
fof(f93,definition,
( spl22_3
<=> ! [X2,X1,X3] :
( ~ model(X1,X2)
| model(X3,X2) ) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f94,plain,
( ! [X2,X3,X1] :
( model(X3,X2)
| ~ model(X1,X2) )
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f113,plain,
( ! [X0] : ~ model(X0,sK6)
| ~ spl22_3 ),
inference(resolution,[],[f94,f64]) ).
fof(f120,plain,
( $false
| ~ spl22_3 ),
inference(resolution,[],[f113,f63]) ).
fof(f121,plain,
~ spl22_3,
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f170,plain,
! [X0,X1] :
( ~ status(X0,X1,wca)
| model(sK0(X0,X1),X0) ),
inference(resolution,[],[f88,f56]) ).
fof(f464,plain,
! [X2,X3,X0,X1] :
( model(sK0(X0,X1),X0)
| model(sK3(X0),X0)
| ~ model(X2,X1)
| model(X3,X1) ),
inference(resolution,[],[f170,f59]) ).
fof(f1998,plain,
! [X2,X0,X1] :
( model(sK3(sK17),sK17)
| ~ model(X0,X1)
| model(X2,X1) ),
inference(resolution,[],[f464,f74]) ).
fof(f2004,definition,
( spl22_122
<=> model(sK3(sK17),sK17) ),
introduced(definition,[new_symbols(definition,[spl22_122])],[avatar_definition]) ).
fof(f2005,plain,
( model(sK3(sK17),sK17)
| ~ spl22_122 ),
inference(avatar_component_clause,[],[f2004]) ).
fof(f2006,plain,
( spl22_3
| spl22_122 ),
inference(avatar_split_clause,[],[f1998,f2004,f93]) ).
fof(f2011,plain,
( $false
| ~ spl22_122 ),
inference(resolution,[],[f2005,f74]) ).
fof(f2012,plain,
~ spl22_122,
inference(avatar_contradiction_clause,[],[f2011]) ).
cnf(s6,plain,
~ spl22_3,
inference(sat_conversion,[],[f121]) ).
cnf(s338,plain,
( spl22_3
| spl22_122 ),
inference(sat_conversion,[],[f2006]) ).
cnf(s339,plain,
~ spl22_122,
inference(sat_conversion,[],[f2012]) ).
cnf(s340,plain,
spl22_3,
inference(rat,[],[s338,s339]) ).
cnf(s404,plain,
$false,
inference(rat,[],[s6,s340]) ).
fof(f2013,plain,
$false,
inference(avatar_sat_refutation,[],[s404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS268+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 13:51:51 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.69/1.27 % (3540507)Detected formulas, will run a generic FOF schedule.
% 2.69/1.27 % (3540518)dis-21_1_sil=8000:lcm=predicate:random_seed=3125035948: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)
% 2.69/1.27 % (3540518)First to succeed.
% 2.69/1.27 % (3540518)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3540507"
% 2.69/1.27 % (3540512)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=80684677:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.27 % (3540517)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3341062364:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.27 % (3540516)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3958206332:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.27 % (3540514)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=1676833512:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.27 % (3540513)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=1647371580:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.27 % (3540515)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4171832653:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.27 % (3540515)Refutation not found, incomplete strategy
% 2.69/1.27 % (3540515)------------------------------
% 2.69/1.27 % (3540515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.27 % (3540515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.27 % (3540515)CaDiCaL version: 2.1.3
% 2.69/1.27 % (3540515)Termination reason: Refutation not found, incomplete strategy
% 2.69/1.27 % (3540515)Time elapsed: 0.001 s
% 2.69/1.27 % (3540515)Peak memory usage: 87 MB
% 2.69/1.27 % (3540516)Also succeeded, but the first one will report.
% 2.69/1.27 % (3540517)Also succeeded, but the first one will report.
% 2.69/1.27 % (3540518)Refutation found. Thanks to Tanya!
% 2.69/1.27 % SZS status Theorem for theBenchmark
% 2.69/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.27 % (3540518)------------------------------
% 2.69/1.27 % (3540518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.27 % (3540518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.27 % (3540518)CaDiCaL version: 2.1.3
% 2.69/1.27 % (3540518)Termination reason: Refutation
% 2.69/1.27 % (3540518)Time elapsed: 0.015 s
% 2.69/1.27 % (3540518)Peak memory usage: 90 MB
% 2.69/1.27 % (3540518)Instructions burned: 42 (million)
% 2.69/1.27 % (3540518)------------------------------
% 2.69/1.27 % (3540518)------------------------------
% 2.69/1.27 % (3540507)Success in time 0.311 s
% 2.69/1.27 % Vampire exiting
%------------------------------------------------------------------------------