%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 2.59s 1.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 16 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 160 ( 67 ~; 62 |; 19 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 93 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
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(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ci4) ).
fof(f11,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(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3) )
=> equal_points(X0,intersection_point(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3) )
=> equal_points(X0,intersection_point(X2,X3)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
=> ~ apart_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
=> equal_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( ~ equal_points(X0,intersection_point(X2,X3))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3) ),
inference(ennf_transformation,[],[f37]) ).
fof(f42,plain,
? [X0,X1,X2,X3] :
( ~ equal_points(X0,intersection_point(X2,X3))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3) ),
inference(flattening,[],[f41]) ).
fof(f45,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,[],[f11]) ).
fof(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f48,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f50,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f54,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f57,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f58,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f59,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f58]) ).
fof(f64,plain,
( ~ equal_points(sK0,intersection_point(sK2,sK3))
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& incident_point_and_line(sK0,sK2)
& incident_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)],[f42]) ).
fof(f65,plain,
incident_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f64]) ).
fof(f66,plain,
incident_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f64]) ).
fof(f67,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f64]) ).
fof(f69,plain,
~ equal_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f64]) ).
fof(f71,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,[],[f46]) ).
fof(f72,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f73,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f74,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f75,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f77,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f78,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f79,plain,
! [X0,X1] :
( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f81,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f82,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f86,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(resolution,[],[f78,f69]) ).
fof(f87,plain,
~ apart_point_and_line(sK0,sK3),
inference(resolution,[],[f79,f65]) ).
fof(f88,plain,
~ apart_point_and_line(sK0,sK2),
inference(resolution,[],[f79,f66]) ).
fof(f98,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f82,f77]) ).
fof(f111,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,[],[f71,f87]) ).
fof(f117,plain,
! [X0] :
( apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,sK2)
| ~ distinct_points(X0,sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(resolution,[],[f111,f88]) ).
fof(f123,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,[],[f117,f74]) ).
fof(f153,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f123,f75]) ).
fof(f158,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(duplicate_literal_removal,[],[f153]) ).
fof(f159,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f158,f81]) ).
fof(f162,plain,
! [X0] :
( ~ distinct_points(X0,intersection_point(sK2,sK3))
| distinct_points(X0,sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(resolution,[],[f159,f72]) ).
fof(f198,plain,
( distinct_points(sK0,sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(resolution,[],[f162,f86]) ).
fof(f206,plain,
~ distinct_lines(sK2,sK3),
inference(forward_subsumption_resolution,[],[f198,f73]) ).
fof(f220,plain,
~ convergent_lines(sK3,sK2),
inference(resolution,[],[f206,f98]) ).
fof(f226,plain,
~ distinct_lines(sK3,sK2),
inference(resolution,[],[f220,f81]) ).
fof(f229,plain,
~ convergent_lines(sK2,sK3),
inference(resolution,[],[f226,f98]) ).
fof(f230,plain,
$false,
inference(forward_subsumption_resolution,[],[f229,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.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 07:28:37 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.59/1.30 % (3170334)Detected formulas, will run a generic FOF schedule.
% 2.59/1.30 % (3170345)dis-21_1_sil=8000:lcm=predicate:random_seed=1044369959: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)
% 2.59/1.30 % (3170345)Instruction limit reached!
% 2.59/1.30 % (3170345)------------------------------
% 2.59/1.30 % (3170345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.30 % (3170345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.30 % (3170345)CaDiCaL version: 2.1.3
% 2.59/1.30 % (3170345)Termination reason: Instruction limit
% 2.59/1.30 % (3170345)Termination phase: Saturation
% 2.59/1.30 % (3170345)Time elapsed: 0.042 s
% 2.59/1.30 % (3170345)Peak memory usage: 89 MB
% 2.59/1.30 % (3170343)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2829645182:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.30 % (3170342)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3047710724:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.30 % (3170345)Instructions burned: 130 (million)
% 2.59/1.30 % (3170344)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1625797273:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.30 % (3170340)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=3161410612:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.30 % (3170341)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=478180734:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.30 % (3170339)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=1725834723:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.30 % (3170342)Refutation not found, incomplete strategy
% 2.59/1.30 % (3170342)------------------------------
% 2.59/1.30 % (3170342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.30 % (3170342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.30 % (3170342)CaDiCaL version: 2.1.3
% 2.59/1.30 % (3170342)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.30 % (3170342)Time elapsed: 0.001 s
% 2.59/1.30 % (3170342)Peak memory usage: 88 MB
% 2.59/1.30 % (3170343)First to succeed.
% 2.59/1.30 % (3170343)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3170334"
% 2.59/1.30 % (3170344)Instruction limit reached!
% 2.59/1.30 % (3170344)------------------------------
% 2.59/1.30 % (3170344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.30 % (3170344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.30 % (3170344)CaDiCaL version: 2.1.3
% 2.59/1.30 % (3170344)Termination reason: Instruction limit
% 2.59/1.30 % (3170344)Termination phase: Saturation
% 2.59/1.30 % (3170344)Time elapsed: 0.086 s
% 2.59/1.30 % (3170344)Peak memory usage: 88 MB
% 2.59/1.30 % (3170344)Instructions burned: 140 (million)
% 2.59/1.30 % (3170353)lrs+10_1_sil=8000:sp=occurrence:random_seed=1489206852:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.59/1.30 % (3170353)Also succeeded, but the first one will report.
% 2.59/1.30 % (3170342)------------------------------
% 2.59/1.30 % (3170342)------------------------------
% 2.59/1.30 % (3170354)lrs+10_1_sil=32000:urr=on:br=off:random_seed=180105219:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.59/1.30 % (3170354)Refutation not found, incomplete strategy
% 2.59/1.30 % (3170354)------------------------------
% 2.59/1.30 % (3170354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.30 % (3170354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.30 % (3170354)CaDiCaL version: 2.1.3
% 2.59/1.30 % (3170354)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.30 % (3170354)Time elapsed: 0.002 s
% 2.59/1.30 % (3170354)Peak memory usage: 88 MB
% 2.59/1.30 % (3170354)Instructions burned: 1 (million)
% 2.59/1.30 % (3170343)Refutation found. Thanks to Tanya!
% 2.59/1.30 % SZS status Theorem for theBenchmark
% 2.59/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3170343)------------------------------
% 0.17/1.50 % (3170343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3170343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3170343)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3170343)Termination reason: Refutation
% 0.17/1.50 % (3170343)Time elapsed: 0.005 s
% 0.17/1.50 % (3170343)Peak memory usage: 88 MB
% 0.17/1.50 % (3170343)Instructions burned: 6 (million)
% 0.17/1.50 % (3170343)------------------------------
% 0.17/1.50 % (3170343)------------------------------
% 0.17/1.50 % (3170334)Success in time 0.44 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------