%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO226+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 : n018.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 09:52:07 AM UTC 2026
% Result : Theorem 3.58s 1.47s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 3 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 14 |; 18 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci4) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4) ).
fof(f36,conjecture,
! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> ? [X2] :
( point(X2)
=> ( incident_point_and_line(X2,X0)
& incident_point_and_line(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> ? [X2] :
( point(X2)
=> ( incident_point_and_line(X2,X0)
& incident_point_and_line(X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
=> incident_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f39,plain,
? [X0,X1] :
( ! [X2] :
( ( ~ incident_point_and_line(X2,X0)
| ~ incident_point_and_line(X2,X1) )
& point(X2) )
& line(X0)
& line(X1)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f40,plain,
? [X0,X1] :
( ! [X2] :
( ( ~ incident_point_and_line(X2,X0)
| ~ incident_point_and_line(X2,X1) )
& point(X2) )
& line(X0)
& line(X1)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f39]) ).
fof(f63,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f74,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f75,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f80,plain,
( ! [X2] :
( ( ~ incident_point_and_line(X2,sK0)
| ~ incident_point_and_line(X2,sK1) )
& point(X2) )
& line(sK0)
& line(sK1)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f40]) ).
fof(f81,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f85,plain,
! [X2] :
( ~ incident_point_and_line(X2,sK1)
| ~ incident_point_and_line(X2,sK0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f106,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f116,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f117,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
! [X0] :
( ~ incident_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f106,f85]) ).
fof(f126,plain,
! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f124,f106]) ).
fof(f128,plain,
! [X0] :
( apart_point_and_line(intersection_point(X0,sK1),sK0)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f126,f116]) ).
fof(f130,plain,
( ~ convergent_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f128,f117]) ).
fof(f131,plain,
~ convergent_lines(sK0,sK1),
inference(duplicate_literal_removal,[],[f130]) ).
fof(f132,plain,
$false,
inference(resolution,[],[f131,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO226+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 07:47:53 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.58/1.47 % (1999454)Detected formulas, will run a generic FOF schedule.
% 3.58/1.47 % (1999462)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2489258466:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.58/1.47 % (1999462)Refutation not found, incomplete strategy
% 3.58/1.47 % (1999462)------------------------------
% 3.58/1.47 % (1999462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.47 % (1999462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.47 % (1999462)CaDiCaL version: 2.1.3
% 3.58/1.47 % (1999462)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.47 % (1999462)Time elapsed: 0.001 s
% 3.58/1.47 % (1999462)Peak memory usage: 87 MB
% 3.58/1.47 % (1999465)dis-21_1_sil=8000:lcm=predicate:random_seed=281418004: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)
% 3.58/1.47 % (1999461)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=4098567676:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.58/1.47 % (1999463)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3167241157:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.58/1.47 % (1999460)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=2938624103:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.58/1.47 % (1999459)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=2591480180:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.58/1.47 % (1999464)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3091489905:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.58/1.47 % (1999463)Refutation not found, incomplete strategy
% 3.58/1.47 % (1999463)------------------------------
% 3.58/1.47 % (1999463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.47 % (1999463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.47 % (1999463)CaDiCaL version: 2.1.3
% 3.58/1.47 % (1999463)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.47 % (1999463)Time elapsed: 0.001 s
% 3.58/1.47 % (1999463)Peak memory usage: 87 MB
% 3.58/1.47 % (1999465)First to succeed.
% 3.58/1.47 % (1999464)Also succeeded, but the first one will report.
% 3.58/1.47 % (1999465)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1999454"
% 3.58/1.47 % (1999462)------------------------------
% 3.58/1.47 % (1999462)------------------------------
% 3.58/1.47 % (1999463)------------------------------
% 3.58/1.47 % (1999463)------------------------------
% 3.58/1.47 % (1999465)Refutation found. Thanks to Tanya!
% 3.58/1.47 % SZS status Theorem for theBenchmark
% 3.58/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.47 % (1999465)------------------------------
% 3.58/1.47 % (1999465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.47 % (1999465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.47 % (1999465)CaDiCaL version: 2.1.3
% 3.58/1.47 % (1999465)Termination reason: Refutation
% 3.58/1.47 % (1999465)Time elapsed: 0.002 s
% 3.58/1.47 % (1999465)Peak memory usage: 88 MB
% 3.58/1.47 % (1999465)Instructions burned: 2 (million)
% 3.58/1.47 % (1999465)------------------------------
% 3.58/1.47 % (1999465)------------------------------
% 3.58/1.47 % (1999454)Success in time 0.426 s
% 3.58/1.47 % Vampire exiting
%------------------------------------------------------------------------------