%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS267+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 : n014.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 2.57s 1.31s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 17 unt; 3 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 67 ~; 52 |; 18 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 83 !; 15 ?)
% 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(f15,axiom,
! [X0,X1] :
( ( ~ ? [X2] : model(X2,X0)
& ! [X3] : model(X3,X1) )
<=> status(X0,X1,tca) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tca) ).
fof(f20,axiom,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& status(X2,X3,X1) )
<=> mighta(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta) ).
fof(f27,axiom,
? [X0] :
! [X1] : model(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tautology) ).
fof(f29,axiom,
? [X0] :
! [X1] : ~ model(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contradiction) ).
fof(f33,conjecture,
mighta(tca,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta_tca_thm) ).
fof(f34,negated_conjecture,
~ mighta(tca,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ mighta(tca,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) )
<=> status(X0,X1,tca) ),
inference(ennf_transformation,[],[f15]) ).
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) )
| ~ status(X0,X1,tca) )
& ( status(X0,X1,tca)
| ? [X2] : model(X2,X0)
| ? [X3] : ~ model(X3,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( ! [X2] : ~ model(X2,X0)
& ! [X3] : model(X3,X1) )
| ~ status(X0,X1,tca) )
& ( status(X0,X1,tca)
| ? [X2] : model(X2,X0)
| ? [X3] : ~ model(X3,X1) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ! [X2] : ~ model(X2,X0)
& ! [X3] : model(X3,X1) )
| ~ status(X0,X1,tca) )
& ( status(X0,X1,tca)
| ? [X4] : model(X4,X0)
| ? [X5] : ~ model(X5,X1) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( ( ! [X2] : ~ model(X2,X0)
& ! [X3] : model(X3,X1) )
| ~ status(X0,X1,tca) )
& ( status(X0,X1,tca)
| model(sK1(X0),X0)
| ~ model(sK2(X1),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X4,sK1(X0)),skolemize(X5,sK2(X1))],[f46]) ).
fof(f51,plain,
! [X1] : ~ model(X1,sK16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f29]) ).
fof(f53,plain,
! [X1] : model(X1,sK20),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f27]) ).
fof(f54,plain,
~ mighta(tca,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(f57,plain,
! [X0,X1] :
( status(X0,X1,thm)
| ~ model(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X0,X1] :
( status(X0,X1,tca)
| model(sK1(X0),X0)
| ~ model(sK2(X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f60,plain,
! [X3,X0,X1] :
( ~ status(X0,X1,tca)
| model(X3,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f73,plain,
! [X1] : ~ model(X1,sK16),
inference(cnf_transformation,[],[f51]) ).
fof(f76,plain,
! [X1] : model(X1,sK20),
inference(cnf_transformation,[],[f53]) ).
fof(f87,plain,
! [X0,X1] :
( ~ status(X0,X1,tca)
| ~ status(X0,X1,thm) ),
inference(resolution,[],[f55,f54]) ).
fof(f88,plain,
! [X0,X1] :
( ~ status(X0,X1,thm)
| ~ model(sK2(X1),X1)
| model(sK1(X0),X0) ),
inference(resolution,[],[f59,f87]) ).
fof(f90,plain,
! [X2,X0,X1] :
( model(sK1(X0),X0)
| ~ model(sK2(X1),X1)
| model(X2,X1) ),
inference(resolution,[],[f59,f60]) ).
fof(f92,definition,
( spl21_3
<=> ! [X2,X1] :
( ~ model(sK2(X1),X1)
| model(X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
fof(f93,plain,
( ! [X2,X1] :
( model(X2,X1)
| ~ model(sK2(X1),X1) )
| ~ spl21_3 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,definition,
( spl21_4
<=> ! [X0] : model(sK1(X0),X0) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
fof(f96,plain,
( ! [X0] : model(sK1(X0),X0)
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f97,plain,
( spl21_3
| spl21_4 ),
inference(avatar_split_clause,[],[f90,f95,f92]) ).
fof(f99,definition,
( spl21_5
<=> ! [X1] : ~ model(sK2(X1),X1) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f100,plain,
( ! [X1] : ~ model(sK2(X1),X1)
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f105,plain,
( $false
| ~ spl21_5 ),
inference(resolution,[],[f100,f76]) ).
fof(f107,plain,
~ spl21_5,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f122,plain,
! [X0,X1] :
( model(sK1(X1),X1)
| ~ model(sK2(X0),X0)
| ~ model(sK0(X1,X0),X0) ),
inference(resolution,[],[f88,f57]) ).
fof(f176,plain,
( $false
| ~ spl21_4 ),
inference(resolution,[],[f96,f73]) ).
fof(f177,plain,
~ spl21_4,
inference(avatar_contradiction_clause,[],[f176]) ).
fof(f211,plain,
! [X0] :
( ~ model(sK0(sK16,X0),X0)
| ~ model(sK2(X0),X0) ),
inference(resolution,[],[f122,f73]) ).
fof(f410,plain,
( ! [X0] :
( ~ model(sK2(X0),X0)
| ~ model(sK2(X0),X0) )
| ~ spl21_3 ),
inference(resolution,[],[f211,f93]) ).
fof(f412,plain,
( ! [X0] : ~ model(sK2(X0),X0)
| ~ spl21_3 ),
inference(duplicate_literal_removal,[],[f410]) ).
fof(f413,plain,
( spl21_5
| ~ spl21_3 ),
inference(avatar_split_clause,[],[f412,f92,f99]) ).
cnf(s2,plain,
( spl21_3
| spl21_4 ),
inference(sat_conversion,[],[f97]) ).
cnf(s4,plain,
~ spl21_5,
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
~ spl21_4,
inference(sat_conversion,[],[f177]) ).
cnf(s37,plain,
( ~ spl21_3
| spl21_5 ),
inference(sat_conversion,[],[f413]) ).
cnf(s50,plain,
~ spl21_3,
inference(rat,[],[s37,s4]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s2,s8,s50]) ).
fof(f414,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS267+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 13:48:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.57/1.31 % (826936)Detected formulas, will run a generic FOF schedule.
% 2.57/1.31 % (826947)dis-21_1_sil=8000:lcm=predicate:random_seed=720754766: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)
% 2.57/1.31 % (826947)First to succeed.
% 2.57/1.31 % (826947)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-826936"
% 2.57/1.31 % (826946)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1803149375:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.31 % (826945)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1735872852:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.31 % (826944)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3903123583:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.31 % (826941)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=2438166673:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.31 % (826942)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=339930895:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.31 % (826943)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=3763055457:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.31 % (826944)Refutation not found, incomplete strategy
% 2.57/1.31 % (826944)------------------------------
% 2.57/1.31 % (826944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.31 % (826944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.31 % (826944)CaDiCaL version: 2.1.3
% 2.57/1.31 % (826944)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.31 % (826944)Time elapsed: 0.001 s
% 2.57/1.31 % (826944)Peak memory usage: 88 MB
% 2.57/1.31 % (826945)Also succeeded, but the first one will report.
% 2.57/1.31 % (826946)Also succeeded, but the first one will report.
% 2.57/1.31 % (826947)Refutation found. Thanks to Tanya!
% 2.57/1.31 % SZS status Theorem for theBenchmark
% 2.57/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.31 % (826947)------------------------------
% 2.57/1.31 % (826947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.31 % (826947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.31 % (826947)CaDiCaL version: 2.1.3
% 2.57/1.31 % (826947)Termination reason: Refutation
% 2.57/1.31 % (826947)Time elapsed: 0.004 s
% 2.57/1.31 % (826947)Peak memory usage: 89 MB
% 2.57/1.31 % (826947)Instructions burned: 7 (million)
% 2.57/1.31 % (826947)------------------------------
% 2.57/1.31 % (826947)------------------------------
% 2.57/1.31 % (826936)Success in time 0.274 s
% 2.57/1.31 % Vampire exiting
%------------------------------------------------------------------------------