%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO205+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 : n011.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 09:52:00 AM UTC 2026
% Result : Theorem 2.76s 1.27s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 13 unt; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 179 ( 77 ~; 79 |; 11 &)
% ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 107 ( 101 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
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(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/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& equal_lines(X1,X2) )
=> ( convergent_lines(X0,X2)
& equal_points(intersection_point(X0,X1),intersection_point(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& equal_lines(X1,X2) )
=> ( convergent_lines(X0,X2)
& equal_points(intersection_point(X0,X1),intersection_point(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( equal_lines(X0,X1)
=> ~ distinct_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
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] :
( ( ~ convergent_lines(X0,X2)
| ~ equal_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
& convergent_lines(X0,X1)
& equal_lines(X1,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ( ~ convergent_lines(X0,X2)
| ~ equal_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
& convergent_lines(X0,X1)
& equal_lines(X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f47,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f48,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| ~ equal_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f51,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(f52,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,[],[f51]) ).
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(f60,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f61,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f60]) ).
fof(f64,plain,
( ( ~ convergent_lines(sK0,sK2)
| ~ equal_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) )
& convergent_lines(sK0,sK1)
& equal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f42]) ).
fof(f65,plain,
equal_lines(sK1,sK2),
inference(cnf_transformation,[],[f64]) ).
fof(f66,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f64]) ).
fof(f67,plain,
( ~ equal_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f69,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f71,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f72,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f73,plain,
! [X0,X1] :
( ~ equal_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f75,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,[],[f52]) ).
fof(f79,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f80,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f81,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f84,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(resolution,[],[f72,f67]) ).
fof(f85,plain,
~ distinct_lines(sK1,sK2),
inference(resolution,[],[f73,f65]) ).
fof(f91,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f80,f71]) ).
fof(f93,plain,
~ convergent_lines(sK2,sK1),
inference(resolution,[],[f91,f85]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(intersection_point(X2,X1),X0)
| distinct_lines(X0,X1)
| ~ convergent_lines(X2,X1) ),
inference(resolution,[],[f81,f68]) ).
fof(f98,plain,
~ distinct_lines(sK2,sK1),
inference(resolution,[],[f93,f79]) ).
fof(f99,plain,
~ convergent_lines(sK1,sK2),
inference(resolution,[],[f98,f91]) ).
fof(f103,plain,
! [X0] :
( distinct_lines(X0,sK2)
| ~ convergent_lines(sK1,X0) ),
inference(resolution,[],[f99,f80]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(intersection_point(X2,X1),X3)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X3)
| ~ distinct_points(X0,intersection_point(X2,X1))
| ~ distinct_lines(X3,X1)
| ~ convergent_lines(X2,X1) ),
inference(resolution,[],[f75,f68]) ).
fof(f132,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,intersection_point(X2,X1))
| ~ distinct_lines(X2,X1)
| ~ convergent_lines(X2,X1)
| ~ convergent_lines(X2,X1) ),
inference(resolution,[],[f110,f69]) ).
fof(f139,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,intersection_point(X2,X1))
| ~ distinct_lines(X2,X1)
| ~ convergent_lines(X2,X1) ),
inference(duplicate_literal_removal,[],[f132]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,intersection_point(X2,X1))
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X2,X1) ),
inference(forward_subsumption_resolution,[],[f139,f79]) ).
fof(f162,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ distinct_lines(sK0,sK2)
| ~ convergent_lines(sK0,sK2) ),
inference(resolution,[],[f141,f84]) ).
fof(f170,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f162,f79]) ).
fof(f174,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK0,sK2)
| distinct_lines(sK2,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f170,f94]) ).
fof(f175,plain,
( ~ distinct_lines(sK0,sK2)
| distinct_lines(sK2,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f174,f69]) ).
fof(f179,plain,
( ~ distinct_lines(sK0,sK2)
| ~ convergent_lines(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f175,f98]) ).
fof(f183,plain,
~ distinct_lines(sK0,sK2),
inference(forward_subsumption_resolution,[],[f179,f66]) ).
fof(f195,plain,
~ convergent_lines(sK1,sK0),
inference(resolution,[],[f183,f103]) ).
fof(f230,plain,
~ distinct_lines(sK1,sK0),
inference(resolution,[],[f195,f79]) ).
fof(f260,plain,
~ convergent_lines(sK0,sK1),
inference(resolution,[],[f230,f91]) ).
fof(f261,plain,
$false,
inference(forward_subsumption_resolution,[],[f260,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:36:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.76/1.27 % (2067485)Detected formulas, will run a generic FOF schedule.
% 2.76/1.27 % (2067595)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2621369402:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.27 % (2067595)Refutation not found, incomplete strategy
% 2.76/1.27 % (2067595)------------------------------
% 2.76/1.27 % (2067595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.27 % (2067595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.27 % (2067595)CaDiCaL version: 2.1.3
% 2.76/1.27 % (2067595)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.27 % (2067595)Time elapsed: 0.0000 s
% 2.76/1.27 % (2067595)Peak memory usage: 87 MB
% 2.76/1.27 % (2067593)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=447625140:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.27 % (2067592)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=3661566819:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.27 % (2067598)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=759401057:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.27 % (2067596)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1895160474:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.27 % (2067594)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=860045610:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.27 % (2067596)First to succeed.
% 2.76/1.27 % (2067596)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2067485"
% 2.76/1.27 % (2067599)dis-21_1_sil=8000:lcm=predicate:random_seed=4164442443: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)
% 2.76/1.27 % (2067598)Also succeeded, but the first one will report.
% 2.76/1.27 % (2067599)Also succeeded, but the first one will report.
% 2.76/1.27 % (2067595)------------------------------
% 2.76/1.27 % (2067595)------------------------------
% 2.76/1.27 % (2067611)lrs+10_1_sil=8000:sp=occurrence:random_seed=3426577046:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.76/1.27 % (2067596)Refutation found. Thanks to Tanya!
% 2.76/1.27 % SZS status Theorem for theBenchmark
% 2.76/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.46 % (2067596)------------------------------
% 3.51/1.46 % (2067596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.46 % (2067596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.46 % (2067596)CaDiCaL version: 2.1.3
% 3.51/1.46 % (2067596)Termination reason: Refutation
% 3.51/1.46 % (2067596)Time elapsed: 0.007 s
% 3.51/1.46 % (2067596)Peak memory usage: 88 MB
% 3.51/1.46 % (2067596)Instructions burned: 7 (million)
% 3.51/1.46 % (2067596)------------------------------
% 3.51/1.46 % (2067596)------------------------------
% 3.51/1.46 % (2067485)Success in time 0.41 s
% 3.51/1.46 % Vampire exiting
%------------------------------------------------------------------------------