%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS235+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 11:41:56 AM UTC 2026
% Result : Theorem 3.51s 1.39s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 129 ( 49 ~; 43 |; 28 &)
% ( 4 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 65 !; 12 ?)
% 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(f19,axiom,
! [X0,X1] :
( ( ? [X2] :
( model(X2,X0)
& model(X2,X1) )
& ? [X3] :
( model(X3,X0)
& model(X3,not(X1)) ) )
<=> status(X0,X1,noc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noc) ).
fof(f23,axiom,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
=> ~ status(X2,X3,X1) )
<=> nevera(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nevera) ).
fof(f25,axiom,
! [X0,X1] :
( model(X0,X1)
<~> model(X0,not(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',completeness) ).
fof(f33,conjecture,
nevera(noc,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nevera_noc_thm) ).
fof(f34,negated_conjecture,
~ nevera(noc,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ nevera(noc,thm),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
=> ~ status(X2,X3,X1) )
=> nevera(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f39,plain,
! [X0,X1] :
( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
<=> status(X0,X1,thm) ),
inference(ennf_transformation,[],[f5]) ).
fof(f46,plain,
! [X0,X1] :
( nevera(X0,X1)
| ? [X2,X3] :
( status(X2,X3,X1)
& status(X2,X3,X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f62,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,[],[f39]) ).
fof(f63,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,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
| ~ status(X0,X1,thm) )
& ( status(X0,X1,thm)
| ( ~ model(sK9(X0,X1),X1)
& model(sK9(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1))],[f63]) ).
fof(f114,plain,
! [X0,X1] :
( ( ( ? [X2] :
( model(X2,X0)
& model(X2,X1) )
& ? [X3] :
( model(X3,X0)
& model(X3,not(X1)) ) )
| ~ status(X0,X1,noc) )
& ( status(X0,X1,noc)
| ! [X2] :
( ~ model(X2,X0)
| ~ model(X2,X1) )
| ! [X3] :
( ~ model(X3,X0)
| ~ model(X3,not(X1)) ) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f115,plain,
! [X0,X1] :
( ( ( ? [X2] :
( model(X2,X0)
& model(X2,X1) )
& ? [X3] :
( model(X3,X0)
& model(X3,not(X1)) ) )
| ~ status(X0,X1,noc) )
& ( status(X0,X1,noc)
| ! [X2] :
( ~ model(X2,X0)
| ~ model(X2,X1) )
| ! [X3] :
( ~ model(X3,X0)
| ~ model(X3,not(X1)) ) ) ),
inference(flattening,[],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( ( ( ? [X2] :
( model(X2,X0)
& model(X2,X1) )
& ? [X3] :
( model(X3,X0)
& model(X3,not(X1)) ) )
| ~ status(X0,X1,noc) )
& ( status(X0,X1,noc)
| ! [X4] :
( ~ model(X4,X0)
| ~ model(X4,X1) )
| ! [X5] :
( ~ model(X5,X0)
| ~ model(X5,not(X1)) ) ) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ( ( model(sK39(X0,X1),X0)
& model(sK39(X0,X1),X1)
& model(sK40(X0,X1),X0)
& model(sK40(X0,X1),not(X1)) )
| ~ status(X0,X1,noc) )
& ( status(X0,X1,noc)
| ! [X4] :
( ~ model(X4,X0)
| ~ model(X4,X1) )
| ! [X5] :
( ~ model(X5,X0)
| ~ model(X5,not(X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39,sK40]),skolemize(X2,sK39(X0,X1)),skolemize(X3,sK40(X0,X1))],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( nevera(X0,X1)
| ( status(sK41(X0,X1),sK42(X0,X1),X1)
& status(sK41(X0,X1),sK42(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42]),skolemize(X2,sK41(X0,X1)),skolemize(X3,sK42(X0,X1))],[f46]) ).
fof(f119,plain,
! [X0,X1] :
( ( ~ model(X0,not(X1))
| ~ model(X0,X1) )
& ( model(X0,not(X1))
| model(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ status(X0,X1,thm)
| ~ model(X2,X0)
| model(X2,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f196,plain,
! [X0,X1] :
( model(sK40(X0,X1),not(X1))
| ~ status(X0,X1,noc) ),
inference(cnf_transformation,[],[f117]) ).
fof(f197,plain,
! [X0,X1] :
( model(sK40(X0,X1),X0)
| ~ status(X0,X1,noc) ),
inference(cnf_transformation,[],[f117]) ).
fof(f200,plain,
! [X0,X1] :
( nevera(X0,X1)
| status(sK41(X0,X1),sK42(X0,X1),X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f201,plain,
! [X0,X1] :
( nevera(X0,X1)
| status(sK41(X0,X1),sK42(X0,X1),X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f203,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f221,plain,
~ nevera(noc,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f235,plain,
status(sK41(noc,thm),sK42(noc,thm),noc),
inference(resolution,[],[f200,f221]) ).
fof(f237,plain,
status(sK41(noc,thm),sK42(noc,thm),thm),
inference(resolution,[],[f201,f221]) ).
fof(f238,plain,
! [X0] :
( model(X0,sK42(noc,thm))
| ~ model(X0,sK41(noc,thm)) ),
inference(resolution,[],[f237,f142]) ).
fof(f247,plain,
! [X0,X1] :
( ~ status(X0,X1,noc)
| ~ model(sK40(X0,X1),X1) ),
inference(resolution,[],[f203,f196]) ).
fof(f253,plain,
~ model(sK40(sK41(noc,thm),sK42(noc,thm)),sK42(noc,thm)),
inference(resolution,[],[f247,f235]) ).
fof(f254,plain,
~ model(sK40(sK41(noc,thm),sK42(noc,thm)),sK41(noc,thm)),
inference(resolution,[],[f253,f238]) ).
fof(f257,plain,
~ status(sK41(noc,thm),sK42(noc,thm),noc),
inference(resolution,[],[f254,f197]) ).
fof(f258,plain,
$false,
inference(forward_subsumption_resolution,[],[f257,f235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS235+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n026.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 13:46:56 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
% 3.51/1.39 % (2857920)Detected formulas, will run a generic FOF schedule.
% 3.51/1.39 % (2857925)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=1904259416:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.51/1.39 % (2857931)dis-21_1_sil=8000:lcm=predicate:random_seed=1892583458: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)
% 3.51/1.39 % (2857930)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2856542123:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.51/1.39 % (2857926)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=331853844:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.51/1.39 % (2857927)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=4292101866:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.51/1.39 % (2857929)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1551185168:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.51/1.39 % (2857928)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1514908655:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.51/1.39 % (2857928)Refutation not found, incomplete strategy
% 3.51/1.39 % (2857928)------------------------------
% 3.51/1.39 % (2857928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (2857928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (2857928)CaDiCaL version: 2.1.3
% 3.51/1.39 % (2857928)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.39 % (2857928)Time elapsed: 0.001 s
% 3.51/1.39 % (2857928)Peak memory usage: 87 MB
% 3.51/1.39 % (2857928)Instructions burned: 1 (million)
% 3.51/1.39 % (2857930)First to succeed.
% 3.51/1.39 % (2857930)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2857920"
% 3.51/1.39 % (2857929)Also succeeded, but the first one will report.
% 3.51/1.39 % (2857931)Also succeeded, but the first one will report.
% 3.51/1.39 % (2857928)------------------------------
% 3.51/1.39 % (2857928)------------------------------
% 3.51/1.39 % (2857930)Refutation found. Thanks to Tanya!
% 3.51/1.39 % SZS status Theorem for theBenchmark
% 3.51/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.39 % (2857930)------------------------------
% 3.51/1.39 % (2857930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (2857930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (2857930)CaDiCaL version: 2.1.3
% 3.51/1.39 % (2857930)Termination reason: Refutation
% 3.51/1.39 % (2857930)Time elapsed: 0.006 s
% 3.51/1.39 % (2857930)Peak memory usage: 88 MB
% 3.51/1.39 % (2857930)Instructions burned: 7 (million)
% 3.51/1.39 % (2857930)------------------------------
% 3.51/1.39 % (2857930)------------------------------
% 3.51/1.39 % (2857920)Success in time 0.433 s
% 3.51/1.39 % Vampire exiting
%------------------------------------------------------------------------------