%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO186+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 : n001.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 09:51:52 AM UTC 2026
% Result : Theorem 3.46s 1.47s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 143 ( 60 ~; 55 |; 21 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 68 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
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(f9,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f13,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) )
=> ~ distinct_points(X0,intersection_point(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) )
=> ~ distinct_points(X0,intersection_point(X2,X3)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( distinct_points(X0,intersection_point(X2,X3))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( distinct_points(X0,intersection_point(X2,X3))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,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(f20,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,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f28]) ).
fof(f32,plain,
( distinct_points(sK0,intersection_point(sK2,sK3))
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16]) ).
fof(f33,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f32]) ).
fof(f34,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f35,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f32]) ).
fof(f37,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f32]) ).
fof(f38,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f41,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f42,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(cnf_transformation,[],[f29]) ).
fof(f62,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f40,f39]) ).
fof(f65,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f41,f39]) ).
fof(f66,plain,
! [X0,X1] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,X1)
| ~ distinct_points(X0,sK0)
| ~ distinct_lines(X1,sK3) ),
inference(resolution,[],[f47,f33]) ).
fof(f70,plain,
! [X0] :
( apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,sK2)
| ~ distinct_points(X0,sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(resolution,[],[f66,f34]) ).
fof(f76,plain,
! [X0] :
( apart_point_and_line(intersection_point(X0,sK3),sK2)
| ~ distinct_points(intersection_point(X0,sK3),sK0)
| ~ distinct_lines(sK2,sK3)
| ~ convergent_lines(X0,sK3) ),
inference(resolution,[],[f70,f62]) ).
fof(f84,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f76,f65]) ).
fof(f85,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(duplicate_literal_removal,[],[f84]) ).
fof(f86,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ convergent_lines(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f85,f42]) ).
fof(f87,plain,
~ distinct_points(intersection_point(sK2,sK3),sK0),
inference(forward_subsumption_resolution,[],[f86,f35]) ).
fof(f97,plain,
! [X0] :
( ~ distinct_points(X0,intersection_point(sK2,sK3))
| distinct_points(X0,sK0) ),
inference(resolution,[],[f87,f38]) ).
fof(f128,plain,
distinct_points(sK0,sK0),
inference(resolution,[],[f97,f37]) ).
fof(f132,plain,
$false,
inference(forward_subsumption_resolution,[],[f128,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n001.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 07:34:00 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 3.46/1.47 % (3223703)Detected formulas, will run a generic FOF schedule.
% 3.46/1.47 % (3223811)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=406189106:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.47 % (3223811)Refutation not found, incomplete strategy
% 3.46/1.47 % (3223811)------------------------------
% 3.46/1.47 % (3223811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.47 % (3223811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.47 % (3223811)CaDiCaL version: 2.1.3
% 3.46/1.47 % (3223811)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.47 % (3223811)Time elapsed: 0.0000 s
% 3.46/1.47 % (3223811)Peak memory usage: 87 MB
% 3.46/1.47 % (3223808)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=3933585147:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.47 % (3223813)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1922603906:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.47 % (3223812)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=669609807:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.47 % (3223812)First to succeed.
% 3.46/1.47 % (3223809)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=618210102:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.47 % (3223810)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=4160044223:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.47 % (3223812)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3223703"
% 3.46/1.47 % (3223813)Also succeeded, but the first one will report.
% 3.46/1.47 % (3223814)dis-21_1_sil=8000:lcm=predicate:random_seed=3947062634: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)
% 3.46/1.47 % (3223814)Also succeeded, but the first one will report.
% 3.46/1.47 % (3223811)------------------------------
% 3.46/1.47 % (3223811)------------------------------
% 3.46/1.47 % (3223822)lrs+10_1_sil=8000:sp=occurrence:random_seed=1458575039:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.46/1.47 % (3223822)Also succeeded, but the first one will report.
% 3.46/1.47 % (3223812)Refutation found. Thanks to Tanya!
% 3.46/1.47 % SZS status Theorem for theBenchmark
% 3.46/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.47 % (3223812)------------------------------
% 3.46/1.47 % (3223812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.47 % (3223812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.47 % (3223812)CaDiCaL version: 2.1.3
% 3.46/1.47 % (3223812)Termination reason: Refutation
% 3.46/1.47 % (3223812)Time elapsed: 0.004 s
% 3.46/1.47 % (3223812)Peak memory usage: 88 MB
% 3.46/1.47 % (3223812)Instructions burned: 4 (million)
% 3.46/1.47 % (3223812)------------------------------
% 3.46/1.47 % (3223812)------------------------------
% 3.46/1.47 % (3223703)Success in time 0.399 s
% 3.46/1.47 % Vampire exiting
%------------------------------------------------------------------------------