%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO237+3 : TPTP v9.3.1. Released v4.0.0.
% 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 09:52:10 AM UTC 2026
% Result : Theorem 2.66s 1.34s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 8 unt; 2 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 23 |; 15 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 28 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( right_apart_point(X0,X1)
<=> left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_defns) ).
fof(f6,axiom,
! [X0,X1] :
( apart_point_and_line(X0,X1)
<=> ( left_apart_point(X0,X1)
| right_apart_point(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_defns) ).
fof(f20,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_basics) ).
fof(f37,conjecture,
! [X0,X1,X2,X3] :
( apart_point_and_line(X2,X3)
=> ( divides_points(X3,X0,X1)
=> ( divides_points(X3,X0,X2)
| divides_points(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( apart_point_and_line(X2,X3)
=> ( divides_points(X3,X0,X1)
=> ( divides_points(X3,X0,X2)
| divides_points(X3,X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f40,plain,
? [X0,X1,X2,X3] :
( ~ divides_points(X3,X0,X2)
& ~ divides_points(X3,X1,X2)
& divides_points(X3,X0,X1)
& apart_point_and_line(X2,X3) ),
inference(ennf_transformation,[],[f38]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( ~ divides_points(X3,X0,X2)
& ~ divides_points(X3,X1,X2)
& divides_points(X3,X0,X1)
& apart_point_and_line(X2,X3) ),
inference(flattening,[],[f40]) ).
fof(f54,plain,
! [X0,X1] :
( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f76,plain,
( ~ divides_points(sK3,sK0,sK2)
& ~ divides_points(sK3,sK1,sK2)
& divides_points(sK3,sK0,sK1)
& apart_point_and_line(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f41]) ).
fof(f77,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ right_apart_point(X0,X1) ) )
& ( left_apart_point(X0,X1)
| right_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f78,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ right_apart_point(X0,X1) ) )
& ( left_apart_point(X0,X1)
| right_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ) ),
inference(flattening,[],[f77]) ).
fof(f81,plain,
! [X0,X1] :
( ( right_apart_point(X0,X1)
| ~ left_apart_point(X0,reverse_line(X1)) )
& ( left_apart_point(X0,reverse_line(X1))
| ~ right_apart_point(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f82,plain,
apart_point_and_line(sK2,sK3),
inference(cnf_transformation,[],[f76]) ).
fof(f91,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| right_apart_point(X0,X1)
| left_apart_point(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f110,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f54]) ).
fof(f117,plain,
! [X0,X1] :
( ~ right_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f138,plain,
( right_apart_point(sK2,sK3)
| left_apart_point(sK2,sK3) ),
inference(resolution,[],[f91,f82]) ).
fof(f141,definition,
( spl4_1
<=> left_apart_point(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f142,plain,
( left_apart_point(sK2,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,definition,
( spl4_2
<=> right_apart_point(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f145,plain,
( right_apart_point(sK2,sK3)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f146,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f138,f144,f141]) ).
fof(f147,plain,
( left_apart_point(sK2,reverse_line(sK3))
| ~ spl4_2 ),
inference(resolution,[],[f145,f117]) ).
fof(f148,plain,
( $false
| ~ spl4_2 ),
inference(resolution,[],[f147,f110]) ).
fof(f149,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f148]) ).
fof(f150,plain,
( $false
| ~ spl4_1 ),
inference(resolution,[],[f142,f110]) ).
fof(f151,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f150]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f146]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f149]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f151]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f152,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO237+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:43:35 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 2.66/1.34 % (2220164)Detected formulas, will run a generic FOF schedule.
% 2.66/1.34 % (2220175)dis-21_1_sil=8000:lcm=predicate:random_seed=3442103891: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)
% 2.66/1.34 % (2220175)First to succeed.
% 2.66/1.34 % (2220175)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2220164"
% 2.66/1.34 % (2220169)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=3342687476:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.34 % (2220174)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2614391429:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.34 % (2220172)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2591972419:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.34 % (2220173)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3755086672:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.34 % (2220171)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=491160924:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.34 % (2220170)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=2303767722:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.34 % (2220173)Also succeeded, but the first one will report.
% 2.66/1.34 % (2220172)Refutation not found, incomplete strategy
% 2.66/1.34 % (2220172)------------------------------
% 2.66/1.34 % (2220172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.34 % (2220172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.34 % (2220172)CaDiCaL version: 2.1.3
% 2.66/1.34 % (2220172)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.34 % (2220172)Time elapsed: 0.001 s
% 2.66/1.34 % (2220172)Peak memory usage: 88 MB
% 2.66/1.34 % (2220172)Instructions burned: 1 (million)
% 2.66/1.34 % (2220174)Also succeeded, but the first one will report.
% 2.66/1.34 % (2220175)Refutation found. Thanks to Tanya!
% 2.66/1.34 % SZS status Theorem for theBenchmark
% 2.66/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.34 % (2220175)------------------------------
% 2.66/1.34 % (2220175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.34 % (2220175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.34 % (2220175)CaDiCaL version: 2.1.3
% 2.66/1.34 % (2220175)Termination reason: Refutation
% 2.66/1.34 % (2220175)Time elapsed: 0.002 s
% 2.66/1.34 % (2220175)Peak memory usage: 89 MB
% 2.66/1.34 % (2220175)Instructions burned: 2 (million)
% 2.66/1.34 % (2220175)------------------------------
% 2.66/1.34 % (2220175)------------------------------
% 2.66/1.34 % (2220164)Success in time 0.292 s
% 2.66/1.34 % Vampire exiting
%------------------------------------------------------------------------------