%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO201+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 : n006.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 09:51:58 AM UTC 2026
% Result : Theorem 2.60s 1.25s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 7 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 48 ~; 56 |; 3 &)
% ( 1 <=>; 8 =>; 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 : 77 ( 75 !; 2 ?)
% 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(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(f36,conjecture,
! [X0,X1] :
( convergent_lines(X0,X1)
=> equal_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( convergent_lines(X0,X1)
=> equal_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
=> equal_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f40,plain,
? [X0,X1] :
( ~ equal_points(intersection_point(X0,X1),intersection_point(X1,X0))
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f45,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f48,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(f49,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,[],[f48]) ).
fof(f54,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f55,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f56,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f61,plain,
( ~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0))
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f40]) ).
fof(f62,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f61]) ).
fof(f63,plain,
~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f61]) ).
fof(f64,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f65,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f67,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f68,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f70,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,[],[f49]) ).
fof(f74,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f75,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f79,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(resolution,[],[f68,f63]) ).
fof(f85,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f75,f67]) ).
fof(f94,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,[],[f70,f64]) ).
fof(f101,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,[],[f94,f65]) ).
fof(f106,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,[],[f101]) ).
fof(f108,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,[],[f106,f74]) ).
fof(f134,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK1,sK0) ),
inference(resolution,[],[f108,f79]) ).
fof(f142,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f134,f64]) ).
fof(f150,plain,
( ~ distinct_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f142,f65]) ).
fof(f154,plain,
~ convergent_lines(sK0,sK1),
inference(forward_subsumption_resolution,[],[f150,f85]) ).
fof(f158,plain,
$false,
inference(forward_subsumption_resolution,[],[f154,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:34:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.60/1.25 % (2656352)Detected formulas, will run a generic FOF schedule.
% 2.60/1.25 % (2656361)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2521650016:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.25 % (2656361)First to succeed.
% 2.60/1.25 % (2656361)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2656352"
% 2.60/1.25 % (2656363)dis-21_1_sil=8000:lcm=predicate:random_seed=1627596228: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)
% 2.60/1.25 % (2656358)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=857939180:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.25 % (2656362)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3976613044:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.25 % (2656359)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=4176202170:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.25 % (2656357)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=1460585899:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.25 % (2656360)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1952861777:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.25 % (2656360)Refutation not found, incomplete strategy
% 2.60/1.25 % (2656360)------------------------------
% 2.60/1.25 % (2656360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.25 % (2656360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.25 % (2656360)CaDiCaL version: 2.1.3
% 2.60/1.25 % (2656360)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.25 % (2656360)Time elapsed: 0.001 s
% 2.60/1.25 % (2656360)Peak memory usage: 87 MB
% 2.60/1.25 % (2656362)Also succeeded, but the first one will report.
% 2.60/1.25 % (2656363)Also succeeded, but the first one will report.
% 2.60/1.25 % (2656361)Refutation found. Thanks to Tanya!
% 2.60/1.25 % SZS status Theorem for theBenchmark
% 2.60/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.25 % (2656361)------------------------------
% 2.60/1.25 % (2656361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.25 % (2656361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.25 % (2656361)CaDiCaL version: 2.1.3
% 2.60/1.25 % (2656361)Termination reason: Refutation
% 2.60/1.25 % (2656361)Time elapsed: 0.002 s
% 2.60/1.25 % (2656361)Peak memory usage: 88 MB
% 2.60/1.25 % (2656361)Instructions burned: 4 (million)
% 2.60/1.25 % (2656361)------------------------------
% 2.60/1.25 % (2656361)------------------------------
% 2.60/1.25 % (2656352)Success in time 0.296 s
% 2.60/1.25 % Vampire exiting
%------------------------------------------------------------------------------