%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO228+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 09:52:08 AM UTC 2026
% Result : Theorem 2.58s 1.08s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 5 unt; 3 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 58 ~; 55 |; 11 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
<=> ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con_def) ).
fof(f32,conjecture,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
<=> ( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( ~ convergent_lines(X0,X1)
<=> ( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f70,plain,
? [X0,X1] :
( ~ convergent_lines(X0,X1)
<~> ( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f71,plain,
! [X0,X1] :
( ( convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) )
& ( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
| ~ convergent_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f72,plain,
! [X0,X1] :
( ( convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) )
& ( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
| ~ convergent_lines(X0,X1) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0,X1] :
( ( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
| convergent_lines(X0,X1) )
& ( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ convergent_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f74,plain,
? [X0,X1] :
( ( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
| convergent_lines(X0,X1) )
& ( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ convergent_lines(X0,X1) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
( ( ( unequally_directed_lines(sK0,sK1)
& unequally_directed_lines(sK0,reverse_line(sK1)) )
| convergent_lines(sK0,sK1) )
& ( ~ unequally_directed_lines(sK0,sK1)
| ~ unequally_directed_lines(sK0,reverse_line(sK1))
| ~ convergent_lines(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f74]) ).
fof(f78,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f79,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f80,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f114,plain,
( ~ unequally_directed_lines(sK0,sK1)
| ~ unequally_directed_lines(sK0,reverse_line(sK1))
| ~ convergent_lines(sK0,sK1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f115,plain,
( unequally_directed_lines(sK0,reverse_line(sK1))
| convergent_lines(sK0,sK1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f116,plain,
( unequally_directed_lines(sK0,sK1)
| convergent_lines(sK0,sK1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f118,definition,
( spl2_1
<=> convergent_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f119,plain,
( convergent_lines(sK0,sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( ~ convergent_lines(sK0,sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f122,definition,
( spl2_2
<=> unequally_directed_lines(sK0,reverse_line(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f123,plain,
( unequally_directed_lines(sK0,reverse_line(sK1))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f126,definition,
( spl2_3
<=> unequally_directed_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f127,plain,
( unequally_directed_lines(sK0,sK1)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f114,f126,f122,f118]) ).
fof(f130,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f115,f122,f118]) ).
fof(f131,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f116,f126,f118]) ).
fof(f138,plain,
( ~ unequally_directed_lines(sK0,sK1)
| convergent_lines(sK0,sK1)
| ~ spl2_2 ),
inference(resolution,[],[f80,f123]) ).
fof(f141,plain,
( convergent_lines(sK0,sK1)
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f138,f127]) ).
fof(f142,plain,
( $false
| spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f141,f120]) ).
fof(f143,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f142]) ).
fof(f144,plain,
( unequally_directed_lines(sK0,reverse_line(sK1))
| ~ spl2_1 ),
inference(resolution,[],[f119,f78]) ).
fof(f145,plain,
( unequally_directed_lines(sK0,sK1)
| ~ spl2_1 ),
inference(resolution,[],[f119,f79]) ).
fof(f146,plain,
( spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f144,f118,f122]) ).
fof(f147,plain,
( spl2_3
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f145,f118,f126]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f129]) ).
cnf(s2,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f130]) ).
cnf(s3,plain,
( spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f131]) ).
cnf(s4,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f143]) ).
cnf(s5,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f146]) ).
cnf(s6,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f147]) ).
cnf(s7,plain,
spl2_1,
inference(rat,[],[s4,s2,s3]) ).
cnf(s8,plain,
spl2_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
spl2_2,
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9,s7]) ).
fof(f148,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO228+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n007.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 07:44:10 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 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
% 2.58/1.08 % (1080401)Detected formulas, will run a generic FOF schedule.
% 2.58/1.08 % (1080411)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3798407384:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.08 % (1080411)First to succeed.
% 2.58/1.08 % (1080411)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1080401"
% 2.58/1.08 % (1080407)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=3186728443:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.08 % (1080408)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=1896314142:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.08 % (1080410)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1880973562:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.08 % (1080412)dis-21_1_sil=8000:lcm=predicate:random_seed=3532034545: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)
% 2.58/1.08 % (1080409)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1303686974:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.08 % (1080406)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=1876484510:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.08 % (1080410)Also succeeded, but the first one will report.
% 2.58/1.08 % (1080409)Also succeeded, but the first one will report.
% 2.58/1.08 % (1080412)Also succeeded, but the first one will report.
% 2.58/1.08 % (1080411)Refutation found. Thanks to Tanya!
% 2.58/1.08 % SZS status Theorem for theBenchmark
% 2.58/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.08 % (1080411)------------------------------
% 2.58/1.08 % (1080411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.08 % (1080411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.08 % (1080411)CaDiCaL version: 2.1.3
% 2.58/1.08 % (1080411)Termination reason: Refutation
% 2.58/1.08 % (1080411)Time elapsed: 0.002 s
% 2.58/1.08 % (1080411)Peak memory usage: 89 MB
% 2.58/1.08 % (1080411)Instructions burned: 3 (million)
% 2.58/1.08 % (1080411)------------------------------
% 2.58/1.08 % (1080411)------------------------------
% 2.58/1.08 % (1080401)Success in time 0.325 s
% 2.58/1.08 % Vampire exiting
%------------------------------------------------------------------------------