%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO227+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 : n004.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 2.51s 1.32s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 12 unt; 3 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 75 ( 33 ~; 22 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 16 ( 0 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0,X1] :
( ( line(X0)
& line(X1) )
=> ( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oag8) ).
fof(f32,conjecture,
! [X0,X1] :
( ( line(X0)
& line(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] :
( ( line(X0)
& line(X1) )
=> ~ ( ~ unequally_directed_lines(X0,X1)
& ~ unequally_directed_lines(X0,reverse_line(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f35,plain,
? [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
& ~ unequally_directed_lines(X0,reverse_line(X1))
& line(X0)
& line(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f36,plain,
? [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
& ~ unequally_directed_lines(X0,reverse_line(X1))
& line(X0)
& line(X1) ),
inference(flattening,[],[f35]) ).
fof(f46,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| ~ line(X0)
| ~ line(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f47,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| ~ line(X0)
| ~ line(X1) ),
inference(flattening,[],[f46]) ).
fof(f72,plain,
( ~ unequally_directed_lines(sK0,sK1)
& ~ unequally_directed_lines(sK0,reverse_line(sK1))
& line(sK0)
& line(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f36]) ).
fof(f73,plain,
line(sK1),
inference(cnf_transformation,[],[f72]) ).
fof(f74,plain,
line(sK0),
inference(cnf_transformation,[],[f72]) ).
fof(f75,plain,
~ unequally_directed_lines(sK0,reverse_line(sK1)),
inference(cnf_transformation,[],[f72]) ).
fof(f76,plain,
~ unequally_directed_lines(sK0,sK1),
inference(cnf_transformation,[],[f72]) ).
fof(f87,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1)
| ~ line(X0)
| ~ line(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f128,plain,
( unequally_directed_lines(sK0,sK1)
| ~ line(sK0)
| ~ line(sK1) ),
inference(resolution,[],[f87,f75]) ).
fof(f130,definition,
( spl2_1
<=> line(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f131,plain,
( ~ line(sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,definition,
( spl2_2
<=> line(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f134,plain,
( ~ line(sK0)
| spl2_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,definition,
( spl2_3
<=> unequally_directed_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f137,plain,
( unequally_directed_lines(sK0,sK1)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f138,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f128,f136,f133,f130]) ).
fof(f139,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f131,f73]) ).
fof(f140,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f141,plain,
( $false
| spl2_2 ),
inference(resolution,[],[f134,f74]) ).
fof(f142,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f141]) ).
fof(f143,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f137,f76]) ).
fof(f144,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f143]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f138]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f140]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f142]) ).
cnf(s4,plain,
~ spl2_3,
inference(sat_conversion,[],[f144]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f145,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO227+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 07:46:07 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.51/1.32 % (3180949)Detected formulas, will run a generic FOF schedule.
% 2.51/1.32 % (3180960)dis-21_1_sil=8000:lcm=predicate:random_seed=692822944: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)
% 2.51/1.32 % (3180960)First to succeed.
% 2.51/1.32 % (3180960)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3180949"
% 2.51/1.32 % (3180958)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3244602452:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.51/1.32 % (3180955)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=282039690:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.51/1.32 % (3180957)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1260286102:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.51/1.32 % (3180954)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=3808022332:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.51/1.32 % (3180956)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=978064357:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.51/1.32 % (3180958)Also succeeded, but the first one will report.
% 2.51/1.32 % (3180957)Also succeeded, but the first one will report.
% 2.51/1.32 % (3180959)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=85178568:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.51/1.32 % (3180959)Also succeeded, but the first one will report.
% 2.51/1.32 % (3180960)Refutation found. Thanks to Tanya!
% 2.51/1.32 % SZS status Theorem for theBenchmark
% 2.51/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/1.32 % (3180960)------------------------------
% 2.51/1.32 % (3180960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.32 % (3180960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.32 % (3180960)CaDiCaL version: 2.1.3
% 2.51/1.32 % (3180960)Termination reason: Refutation
% 2.51/1.32 % (3180960)Time elapsed: 0.002 s
% 2.51/1.32 % (3180960)Peak memory usage: 89 MB
% 2.51/1.32 % (3180960)Instructions burned: 2 (million)
% 2.51/1.32 % (3180960)------------------------------
% 2.51/1.32 % (3180960)------------------------------
% 2.51/1.32 % (3180949)Success in time 0.267 s
% 2.51/1.32 % Vampire exiting
%------------------------------------------------------------------------------