%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 62 ( 21 ~; 15 |; 20 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 33 ( 27 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).
fof(f17,conjecture,
! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> ? [X2] :
( point(X2)
=> ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> ? [X2] :
( point(X2)
=> ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( ! [X2] :
( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
& point(X2) )
& line(X0)
& line(X1)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( ! [X2] :
( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
& point(X2) )
& line(X0)
& line(X1)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f25,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f46,plain,
( ! [X2] :
( ( apart_point_and_line(X2,sK0)
| apart_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)],[f20]) ).
fof(f47,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f46]) ).
fof(f51,plain,
! [X2] :
( apart_point_and_line(X2,sK1)
| apart_point_and_line(X2,sK0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f69,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f78,plain,
! [X0] :
( distinct_points(X0,intersection_point(sK0,sK1))
| ~ apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f54,f47]) ).
fof(f80,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolution,[],[f78,f69]) ).
fof(f81,plain,
! [X0] :
( distinct_points(X0,intersection_point(sK0,sK1))
| ~ apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f55,f47]) ).
fof(f83,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolution,[],[f80,f51]) ).
fof(f86,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolution,[],[f81,f69]) ).
fof(f87,plain,
$false,
inference(resolution,[],[f86,f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n002.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 07:48:36 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/1.50 % (3213534)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (3213543)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1840259915:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (3213543)Refutation not found, incomplete strategy
% 0.17/1.50 % (3213543)------------------------------
% 0.17/1.50 % (3213543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3213543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3213543)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3213543)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3213543)Time elapsed: 0.001 s
% 0.17/1.50 % (3213543)Peak memory usage: 88 MB
% 0.17/1.50 % (3213542)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3417946748:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (3213541)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=2738128815:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (3213539)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=1341791145:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (3213545)dis-21_1_sil=8000:lcm=predicate:random_seed=3457983972: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)
% 0.17/1.50 % (3213544)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2261341813:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (3213540)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=4108897107:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (3213542)Refutation not found, incomplete strategy
% 0.17/1.50 % (3213542)------------------------------
% 0.17/1.50 % (3213542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3213542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3213542)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3213542)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3213542)Time elapsed: 0.001 s
% 0.17/1.50 % (3213542)Peak memory usage: 87 MB
% 0.17/1.50 % (3213545)First to succeed.
% 0.17/1.50 % (3213545)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3213534"
% 0.17/1.50 % (3213544)Also succeeded, but the first one will report.
% 0.17/1.50 % (3213543)------------------------------
% 0.17/1.50 % (3213543)------------------------------
% 0.17/1.50 % (3213542)------------------------------
% 0.17/1.50 % (3213542)------------------------------
% 0.17/1.50 % (3213553)lrs+10_1_sil=8000:sp=occurrence:random_seed=443091396:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.17/1.50 % (3213553)Also succeeded, but the first one will report.
% 0.17/1.50 % (3213545)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3213545)------------------------------
% 0.17/1.50 % (3213545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3213545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3213545)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3213545)Termination reason: Refutation
% 0.17/1.50 % (3213545)Time elapsed: 0.002 s
% 0.17/1.50 % (3213545)Peak memory usage: 88 MB
% 0.17/1.50 % (3213545)Instructions burned: 1 (million)
% 0.17/1.50 % (3213545)------------------------------
% 0.17/1.50 % (3213545)------------------------------
% 0.17/1.50 % (3213534)Success in time 0.431 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------