%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS251+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 : n017.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 11:41:57 AM UTC 2026
% Result : Theorem 3.47s 1.44s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 66 ~; 65 |; 16 &)
% ( 6 <=>; 2 =>; 0 <=; 2 <~>)
% 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 81 !; 9 ?)
% 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(f17,axiom,
! [X0,X1] :
( ? [X2] :
( model(X2,X0)
& model(X2,not(X1)) )
<=> status(X0,X1,csa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',csa) ).
fof(f24,axiom,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
<~> status(X2,X3,X1) )
<=> xora(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xora) ).
fof(f26,axiom,
! [X0,X1] :
( model(X0,X1)
<=> ~ model(X0,not(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not) ).
fof(f33,conjecture,
xora(csa,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xora_csa_thm) ).
fof(f34,negated_conjecture,
~ xora(csa,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ xora(csa,thm),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
<~> status(X2,X3,X1) )
=> xora(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
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] :
( xora(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] :
( xora(X0,X1)
| ? [X2,X3] :
( ( status(X2,X3,X0)
| ~ status(X2,X3,X1) )
& ( status(X2,X3,X1)
| ~ status(X2,X3,X0) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f44,plain,
! [X0,X1] :
( xora(X0,X1)
| ( ( status(sK1(X0,X1),sK2(X0,X1),X0)
| ~ status(sK1(X0,X1),sK2(X0,X1),X1) )
& ( status(sK1(X0,X1),sK2(X0,X1),X1)
| ~ status(sK1(X0,X1),sK2(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1))],[f43]) ).
fof(f45,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(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( ( model(sK3(X0,X1),X0)
& model(sK3(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,[sK3]),skolemize(X2,sK3(X0,X1))],[f46]) ).
fof(f54,plain,
! [X0,X1] :
( ( model(X0,X1)
| model(X0,not(X1)) )
& ( ~ model(X0,not(X1))
| ~ model(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f56,plain,
~ xora(csa,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0,X1] :
( model(sK0(X0,X1),X0)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
! [X0,X1] :
( ~ model(sK0(X0,X1),X1)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f42]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ status(X0,X1,thm)
| ~ model(X2,X0)
| model(X2,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f60,plain,
! [X0,X1] :
( status(sK1(X0,X1),sK2(X0,X1),X1)
| xora(X0,X1)
| ~ status(sK1(X0,X1),sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f61,plain,
! [X0,X1] :
( status(sK1(X0,X1),sK2(X0,X1),X0)
| xora(X0,X1)
| ~ status(sK1(X0,X1),sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f62,plain,
! [X3,X0,X1] :
( status(X0,X1,csa)
| ~ model(X3,X0)
| ~ model(X3,not(X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X0,X1] :
( model(sK3(X0,X1),not(X1))
| ~ status(X0,X1,csa) ),
inference(cnf_transformation,[],[f47]) ).
fof(f64,plain,
! [X0,X1] :
( model(sK3(X0,X1),X0)
| ~ status(X0,X1,csa) ),
inference(cnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f81,plain,
! [X0,X1] :
( model(X0,not(X1))
| model(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f101,plain,
! [X0,X1] :
( ~ model(sK3(X0,X1),X1)
| ~ status(X0,X1,csa) ),
inference(resolution,[],[f63,f80]) ).
fof(f110,plain,
! [X0,X1] :
( ~ status(sK1(X0,thm),sK2(X0,thm),X0)
| xora(X0,thm)
| ~ model(X1,sK1(X0,thm))
| model(X1,sK2(X0,thm)) ),
inference(resolution,[],[f60,f59]) ).
fof(f143,plain,
! [X0,X1] :
( xora(csa,thm)
| ~ model(X0,sK1(csa,thm))
| model(X0,sK2(csa,thm))
| ~ model(X1,sK1(csa,thm))
| ~ model(X1,not(sK2(csa,thm))) ),
inference(resolution,[],[f110,f62]) ).
fof(f146,plain,
! [X0,X1] :
( ~ model(X1,not(sK2(csa,thm)))
| model(X0,sK2(csa,thm))
| ~ model(X1,sK1(csa,thm))
| ~ model(X0,sK1(csa,thm)) ),
inference(forward_subsumption_resolution,[],[f143,f56]) ).
fof(f150,plain,
! [X0,X1] :
( ~ model(sK3(X1,sK2(csa,thm)),sK1(csa,thm))
| model(X0,sK2(csa,thm))
| ~ model(X0,sK1(csa,thm))
| ~ status(X1,sK2(csa,thm),csa) ),
inference(resolution,[],[f146,f63]) ).
fof(f162,plain,
! [X0] :
( ~ model(sK3(X0,sK2(csa,thm)),sK1(csa,thm))
| model(sK3(X0,sK2(csa,thm)),sK2(csa,thm))
| ~ status(X0,sK2(csa,thm),csa) ),
inference(factoring,[],[f150]) ).
fof(f164,plain,
! [X0] :
( ~ model(sK3(X0,sK2(csa,thm)),sK1(csa,thm))
| ~ status(X0,sK2(csa,thm),csa) ),
inference(forward_subsumption_resolution,[],[f162,f101]) ).
fof(f167,plain,
( ~ status(sK1(csa,thm),sK2(csa,thm),csa)
| ~ status(sK1(csa,thm),sK2(csa,thm),csa) ),
inference(resolution,[],[f164,f64]) ).
fof(f168,plain,
~ status(sK1(csa,thm),sK2(csa,thm),csa),
inference(duplicate_literal_removal,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ~ model(X0,not(sK2(csa,thm)))
| ~ model(X0,sK1(csa,thm)) ),
inference(resolution,[],[f168,f62]) ).
fof(f170,plain,
( xora(csa,thm)
| ~ status(sK1(csa,thm),sK2(csa,thm),thm) ),
inference(resolution,[],[f168,f61]) ).
fof(f171,plain,
~ status(sK1(csa,thm),sK2(csa,thm),thm),
inference(forward_subsumption_resolution,[],[f170,f56]) ).
fof(f182,plain,
! [X0] :
( model(X0,sK2(csa,thm))
| ~ model(X0,sK1(csa,thm)) ),
inference(resolution,[],[f169,f81]) ).
fof(f188,plain,
! [X0] :
( ~ model(sK0(X0,sK2(csa,thm)),sK1(csa,thm))
| status(X0,sK2(csa,thm),thm) ),
inference(resolution,[],[f182,f58]) ).
fof(f194,plain,
( status(sK1(csa,thm),sK2(csa,thm),thm)
| status(sK1(csa,thm),sK2(csa,thm),thm) ),
inference(resolution,[],[f188,f57]) ).
fof(f195,plain,
status(sK1(csa,thm),sK2(csa,thm),thm),
inference(duplicate_literal_removal,[],[f194]) ).
fof(f196,plain,
$false,
inference(forward_subsumption_resolution,[],[f195,f171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS251+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:42:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.47/1.44 % (2559034)Detected formulas, will run a generic FOF schedule.
% 3.47/1.44 % (2559041)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=3997392489:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.44 % (2559044)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=867206384:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.44 % (2559039)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=3431579591:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.44 % (2559043)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=821674172:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.44 % (2559042)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3836029821:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.44 % (2559040)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=3269199693:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.44 % (2559042)Refutation not found, incomplete strategy
% 3.47/1.44 % (2559042)------------------------------
% 3.47/1.44 % (2559042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (2559042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (2559042)CaDiCaL version: 2.1.3
% 3.47/1.44 % (2559042)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.44 % (2559042)Time elapsed: 0.001 s
% 3.47/1.44 % (2559042)Peak memory usage: 88 MB
% 3.47/1.44 % (2559043)First to succeed.
% 3.47/1.44 % (2559043)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2559034"
% 3.47/1.44 % (2559045)dis-21_1_sil=8000:lcm=predicate:random_seed=3938517003: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)
% 3.47/1.44 % (2559044)Also succeeded, but the first one will report.
% 3.47/1.44 % (2559045)Also succeeded, but the first one will report.
% 3.47/1.44 % (2559042)------------------------------
% 3.47/1.44 % (2559042)------------------------------
% 3.47/1.44 % (2559043)Refutation found. Thanks to Tanya!
% 3.47/1.44 % SZS status Theorem for theBenchmark
% 3.47/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.44 % (2559043)------------------------------
% 3.47/1.44 % (2559043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (2559043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (2559043)CaDiCaL version: 2.1.3
% 3.47/1.44 % (2559043)Termination reason: Refutation
% 3.47/1.44 % (2559043)Time elapsed: 0.004 s
% 3.47/1.44 % (2559043)Peak memory usage: 88 MB
% 3.47/1.44 % (2559043)Instructions burned: 5 (million)
% 3.47/1.44 % (2559043)------------------------------
% 3.47/1.44 % (2559043)------------------------------
% 3.47/1.44 % (2559034)Success in time 0.408 s
% 3.47/1.44 % Vampire exiting
%------------------------------------------------------------------------------