%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS215+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 3.48s 1.45s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 119 ( 50 ~; 44 |; 18 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 72 !; 12 ?)
% 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(f17,axiom,
! [X0,X1] :
( ? [X2] :
( model(X2,X0)
& model(X2,not(X1)) )
<=> status(X0,X1,csa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',csa) ).
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(f28,axiom,
? [X0] :
( ? [X1] : model(X1,X0)
& ? [X2] : ~ model(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satisfiable) ).
fof(f33,conjecture,
nota(csa,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nota_csa_thm) ).
fof(f34,negated_conjecture,
~ nota(csa,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ nota(csa,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)
& model(X2,not(X1)) )
| ~ status(X0,X1,csa) )
& ( status(X0,X1,csa)
| ! [X2] :
( ~ model(X2,X0)
| ~ model(X2,not(X1)) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f44,plain,
! [X0,X1] :
( ( ? [X2] :
( model(X2,X0)
& model(X2,not(X1)) )
| ~ status(X0,X1,csa) )
& ( status(X0,X1,csa)
| ! [X3] :
( ~ model(X3,X0)
| ~ model(X3,not(X1)) ) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( model(sK1(X0,X1),X0)
& model(sK1(X0,X1),not(X1)) )
| ~ status(X0,X1,csa) )
& ( status(X0,X1,csa)
| ! [X3] :
( ~ model(X3,X0)
| ~ model(X3,not(X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f44]) ).
fof(f50,plain,
( model(sK17,sK16)
& ~ model(sK18,sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f28]) ).
fof(f52,plain,
! [X0,X1] :
( ( model(X0,X1)
| model(X0,not(X1)) )
& ( ~ model(X0,not(X1))
| ~ model(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f54,plain,
~ nota(csa,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ status(X0,X1,thm)
| ~ model(X2,X0)
| model(X2,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( status(X2,X3,X1)
| ~ status(X2,X3,X0)
| nota(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X3,X0,X1] :
( status(X0,X1,csa)
| ~ model(X3,X0)
| ~ model(X3,not(X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f74,plain,
~ model(sK18,sK16),
inference(cnf_transformation,[],[f50]) ).
fof(f77,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f78,plain,
! [X0,X1] :
( model(X0,not(X1))
| model(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( ~ status(X0,X1,X2)
| nota(X2,thm)
| ~ model(X3,X0)
| model(X3,X1) ),
inference(resolution,[],[f58,f57]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( nota(csa,thm)
| ~ model(X0,X1)
| model(X0,X2)
| ~ model(X3,X1)
| ~ model(X3,not(X2)) ),
inference(resolution,[],[f105,f59]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( ~ model(X3,not(X2))
| model(X0,X2)
| ~ model(X3,X1)
| ~ model(X0,X1) ),
inference(forward_subsumption_resolution,[],[f138,f54]) ).
fof(f146,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| model(X0,X1)
| ~ model(X0,not(X1)) ),
inference(factoring,[],[f139]) ).
fof(f147,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| model(X0,X1) ),
inference(duplicate_literal_removal,[],[f146]) ).
fof(f148,plain,
! [X0,X1] : ~ model(X0,not(X1)),
inference(forward_subsumption_resolution,[],[f147,f77]) ).
fof(f152,plain,
! [X0,X1] : model(X0,X1),
inference(resolution,[],[f148,f78]) ).
fof(f171,plain,
$false,
inference(resolution,[],[f152,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS215+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 13:40:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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
% 3.48/1.45 % (2045167)Detected formulas, will run a generic FOF schedule.
% 3.48/1.45 % (2045172)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=4046923065:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.45 % (2045177)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2059819106:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.45 % (2045176)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4103564623:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.45 % (2045174)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=615472998:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.45 % (2045175)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=289999323:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.45 % (2045178)dis-21_1_sil=8000:lcm=predicate:random_seed=1952544482: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)
% 3.48/1.45 % (2045173)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=80142917:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.45 % (2045175)Refutation not found, incomplete strategy
% 3.48/1.45 % (2045175)------------------------------
% 3.48/1.45 % (2045175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.45 % (2045175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.45 % (2045175)CaDiCaL version: 2.1.3
% 3.48/1.45 % (2045175)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.45 % (2045175)Time elapsed: 0.001 s
% 3.48/1.45 % (2045175)Peak memory usage: 88 MB
% 3.48/1.45 % (2045176)First to succeed.
% 3.48/1.45 % (2045176)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2045167"
% 3.48/1.45 % (2045177)Also succeeded, but the first one will report.
% 3.48/1.45 % (2045178)Also succeeded, but the first one will report.
% 3.48/1.45 % (2045175)------------------------------
% 3.48/1.45 % (2045175)------------------------------
% 3.48/1.45 % (2045176)Refutation found. Thanks to Tanya!
% 3.48/1.45 % SZS status Theorem for theBenchmark
% 3.48/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.45 % (2045176)------------------------------
% 3.48/1.45 % (2045176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.45 % (2045176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.45 % (2045176)CaDiCaL version: 2.1.3
% 3.48/1.45 % (2045176)Termination reason: Refutation
% 3.48/1.45 % (2045176)Time elapsed: 0.003 s
% 3.48/1.45 % (2045176)Peak memory usage: 88 MB
% 3.48/1.45 % (2045176)Instructions burned: 3 (million)
% 3.48/1.45 % (2045176)------------------------------
% 3.48/1.45 % (2045176)------------------------------
% 3.48/1.45 % (2045167)Success in time 0.41 s
% 3.48/1.45 % Vampire exiting
%------------------------------------------------------------------------------