%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS202+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 : n026.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 11:41:53 AM UTC 2026
% Result : Theorem 5.54s 2.05s
% Output : Refutation 5.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 130 ( 53 ~; 49 |; 21 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 98 ( 77 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( ? [X2] : model(X2,X0)
<=> ? [X3] : model(X3,X1) )
<=> status(X0,X1,esa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',esa) ).
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(f22,axiom,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& ~ status(X2,X3,X1) )
<=> nota(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nota) ).
fof(f27,axiom,
? [X0] :
! [X1] : model(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tautology) ).
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,
nota(esa,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nota_esa_thm) ).
fof(f34,negated_conjecture,
~ nota(esa,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ nota(esa,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,X0)
| ! [X3] : ~ model(X3,X1) )
& ( ? [X3] : model(X3,X1)
| ! [X2] : ~ model(X2,X0) ) )
| ~ status(X0,X1,esa) )
& ( status(X0,X1,esa)
| ( ( ! [X3] : ~ model(X3,X1)
| ! [X2] : ~ model(X2,X0) )
& ( ? [X3] : model(X3,X1)
| ? [X2] : model(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f41,plain,
! [X0,X1] :
( ( ( ( ? [X2] : model(X2,X0)
| ! [X3] : ~ model(X3,X1) )
& ( ? [X4] : model(X4,X1)
| ! [X5] : ~ model(X5,X0) ) )
| ~ status(X0,X1,esa) )
& ( status(X0,X1,esa)
| ( ( ! [X6] : ~ model(X6,X1)
| ! [X7] : ~ model(X7,X0) )
& ( ? [X8] : model(X8,X1)
| ? [X9] : model(X9,X0) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( ( ( model(sK0(X0),X0)
| ! [X3] : ~ model(X3,X1) )
& ( model(sK1(X1),X1)
| ! [X5] : ~ model(X5,X0) ) )
| ~ status(X0,X1,esa) )
& ( status(X0,X1,esa)
| ( ( ! [X6] : ~ model(X6,X1)
| ! [X7] : ~ model(X7,X0) )
& ( model(sK2(X1),X1)
| model(sK3(X0),X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X2,sK0(X0)),skolemize(X4,sK1(X1)),skolemize(X8,sK2(X1)),skolemize(X9,sK3(X0))],[f41]) ).
fof(f43,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(f44,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,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
| ~ status(X0,X1,thm) )
& ( status(X0,X1,thm)
| ( ~ model(sK4(X0,X1),X1)
& model(sK4(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1))],[f44]) ).
fof(f46,plain,
( model(sK5,sK6)
& ~ model(sK5,sK7)
& model(sK8,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8)],[f32]) ).
fof(f51,plain,
! [X1] : model(X1,sK22),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f27]) ).
fof(f52,plain,
~ nota(esa,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0,X1,X6,X7] :
( status(X0,X1,esa)
| ~ model(X6,X1)
| ~ model(X7,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ status(X0,X1,thm)
| ~ model(X2,X0)
| model(X2,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( status(X2,X3,X1)
| ~ status(X2,X3,X0)
| nota(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f61,plain,
model(sK8,sK7),
inference(cnf_transformation,[],[f46]) ).
fof(f62,plain,
~ model(sK5,sK7),
inference(cnf_transformation,[],[f46]) ).
fof(f75,plain,
! [X1] : model(X1,sK22),
inference(cnf_transformation,[],[f51]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ status(X0,X1,X2)
| nota(X2,thm)
| ~ model(X3,X0)
| model(X3,X1) ),
inference(resolution,[],[f60,f59]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4] :
( nota(esa,thm)
| ~ model(X0,X1)
| model(X0,X2)
| ~ model(X3,X2)
| ~ model(X4,X1) ),
inference(resolution,[],[f92,f54]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4] :
( model(X0,X2)
| ~ model(X0,X1)
| ~ model(X3,X2)
| ~ model(X4,X1) ),
inference(forward_subsumption_resolution,[],[f105,f52]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ model(sK5,X0)
| ~ model(X1,sK7)
| ~ model(X2,X0) ),
inference(resolution,[],[f107,f62]) ).
fof(f122,plain,
! [X0,X1] :
( ~ model(X0,sK7)
| ~ model(X1,sK22) ),
inference(resolution,[],[f114,f75]) ).
fof(f127,plain,
! [X0] : ~ model(X0,sK7),
inference(forward_subsumption_resolution,[],[f122,f75]) ).
fof(f140,plain,
$false,
inference(resolution,[],[f127,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS202+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n026.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 13:41:26 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 5.54/2.05 % (2855664)Detected formulas, will run a generic FOF schedule.
% 5.54/2.05 % (2855669)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=885708020:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.54/2.05 % (2855671)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=575335200:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.54/2.05 % (2855674)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=790327048:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.54/2.05 % (2855670)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=1012781690:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.54/2.05 % (2855672)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=859545164:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.54/2.05 % (2855673)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2233137536:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.54/2.05 % (2855672)Refutation not found, incomplete strategy
% 5.54/2.05 % (2855672)------------------------------
% 5.54/2.05 % (2855672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/2.05 % (2855672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/2.05 % (2855672)CaDiCaL version: 2.1.3
% 5.54/2.05 % (2855672)Termination reason: Refutation not found, incomplete strategy
% 5.54/2.05 % (2855672)Time elapsed: 0.002 s
% 5.54/2.05 % (2855672)Peak memory usage: 88 MB
% 5.54/2.05 % (2855672)Instructions burned: 1 (million)
% 5.54/2.05 % (2855673)First to succeed.
% 5.54/2.05 % (2855673)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2855664"
% 5.54/2.05 % (2855674)Also succeeded, but the first one will report.
% 5.54/2.05 % (2855675)dis-21_1_sil=8000:lcm=predicate:random_seed=2821026835: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)
% 5.54/2.05 % (2855675)Also succeeded, but the first one will report.
% 5.54/2.05 % (2855672)------------------------------
% 5.54/2.05 % (2855672)------------------------------
% 5.54/2.05 % (2855673)Refutation found. Thanks to Tanya!
% 5.54/2.05 % SZS status Theorem for theBenchmark
% 5.54/2.05 % SZS output start Proof for theBenchmark
% See solution above
% 5.54/2.05 % (2855673)------------------------------
% 5.54/2.05 % (2855673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/2.05 % (2855673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/2.05 % (2855673)CaDiCaL version: 2.1.3
% 5.54/2.05 % (2855673)Termination reason: Refutation
% 5.54/2.05 % (2855673)Time elapsed: 0.005 s
% 5.54/2.05 % (2855673)Peak memory usage: 88 MB
% 5.54/2.05 % (2855673)Instructions burned: 3 (million)
% 5.54/2.05 % (2855673)------------------------------
% 5.54/2.05 % (2855673)------------------------------
% 5.54/2.05 % (2855664)Success in time 0.645 s
% 5.54/2.05 % Vampire exiting
%------------------------------------------------------------------------------