%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO237+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 : n013.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 3.54s 1.45s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 52 ( 20 ~; 13 |; 14 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 34 ( 26 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( apart_point_and_line(X0,X1)
<=> ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apt_def) ).
fof(f15,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oag10) ).
fof(f32,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(f33,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)],[f32]) ).
fof(f46,plain,
! [X0,X1] :
( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f68,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,[],[f33]) ).
fof(f69,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,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ) )
& ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1))
| ~ apart_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f71,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ) )
& ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1))
| ~ apart_point_and_line(X0,X1) ) ),
inference(flattening,[],[f70]) ).
fof(f74,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)],[f69]) ).
fof(f75,plain,
! [X0,X1] :
( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1))
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f97,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f46]) ).
fof(f117,plain,
apart_point_and_line(sK2,sK3),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X0,X1] :
( left_apart_point(X0,reverse_line(X1))
| ~ apart_point_and_line(X0,X1) ),
inference(forward_subsumption_resolution,[],[f75,f97]) ).
fof(f122,plain,
! [X0,X1] : ~ apart_point_and_line(X0,X1),
inference(forward_subsumption_resolution,[],[f121,f97]) ).
fof(f123,plain,
$false,
inference(resolution,[],[f122,f117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO237+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 07:47:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 3.54/1.45 % (4091459)Detected formulas, will run a generic FOF schedule.
% 3.54/1.45 % (4091467)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2006911663:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.54/1.45 % (4091467)Refutation not found, incomplete strategy
% 3.54/1.45 % (4091467)------------------------------
% 3.54/1.45 % (4091467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.45 % (4091467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.45 % (4091467)CaDiCaL version: 2.1.3
% 3.54/1.45 % (4091467)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.45 % (4091467)Time elapsed: 0.001 s
% 3.54/1.45 % (4091467)Peak memory usage: 88 MB
% 3.54/1.45 % (4091467)Instructions burned: 1 (million)
% 3.54/1.45 % (4091466)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=3573285363:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.54/1.45 % (4091465)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=1773049689:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.54/1.45 % (4091464)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=2048053663:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.54/1.45 % (4091469)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4220872433:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.54/1.45 % (4091469)First to succeed.
% 3.54/1.45 % (4091468)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3977261505:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.54/1.45 % (4091470)dis-21_1_sil=8000:lcm=predicate:random_seed=2573197530: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)
% 3.54/1.45 % (4091469)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4091459"
% 3.54/1.45 % (4091468)Also succeeded, but the first one will report.
% 3.54/1.45 % (4091470)Also succeeded, but the first one will report.
% 3.54/1.45 % (4091467)------------------------------
% 3.54/1.45 % (4091467)------------------------------
% 3.54/1.45 % (4091478)lrs+10_1_sil=8000:sp=occurrence:random_seed=1607313232:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.54/1.45 % (4091478)Also succeeded, but the first one will report.
% 3.54/1.45 % (4091469)Refutation found. Thanks to Tanya!
% 3.54/1.45 % SZS status Theorem for theBenchmark
% 3.54/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.45 % (4091469)------------------------------
% 3.54/1.45 % (4091469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.45 % (4091469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.45 % (4091469)CaDiCaL version: 2.1.3
% 3.54/1.45 % (4091469)Termination reason: Refutation
% 3.54/1.45 % (4091469)Time elapsed: 0.002 s
% 3.54/1.45 % (4091469)Peak memory usage: 88 MB
% 3.54/1.45 % (4091469)Instructions burned: 2 (million)
% 3.54/1.45 % (4091469)------------------------------
% 3.54/1.45 % (4091469)------------------------------
% 3.54/1.45 % (4091459)Success in time 0.418 s
% 3.54/1.45 % Vampire exiting
%------------------------------------------------------------------------------