%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO176+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:51:48 AM UTC 2026
% Result : Theorem 3.26s 1.43s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 57 ( 21 ~; 17 |; 15 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 23 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',con2) ).
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/sandbox/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(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(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)
| apart_point_and_line(sK0,sK2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f34,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f32]) ).
fof(f36,plain,
~ distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f32]) ).
fof(f39,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(f40,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(f74,plain,
( ~ apart_point_and_line(sK0,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f39,f36]) ).
fof(f81,plain,
~ apart_point_and_line(sK0,sK3),
inference(forward_subsumption_resolution,[],[f74,f34]) ).
fof(f82,plain,
apart_point_and_line(sK0,sK2),
inference(resolution,[],[f81,f33]) ).
fof(f85,plain,
( ~ apart_point_and_line(sK0,sK2)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f40,f36]) ).
fof(f92,plain,
~ apart_point_and_line(sK0,sK2),
inference(forward_subsumption_resolution,[],[f85,f34]) ).
fof(f95,plain,
$false,
inference(forward_subsumption_resolution,[],[f82,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO176+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n026.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 07:26:41 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 3.26/1.43 % (2491060)Detected formulas, will run a generic FOF schedule.
% 3.26/1.43 % (2491069)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4222810032:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.26/1.43 % (2491069)First to succeed.
% 3.26/1.43 % (2491069)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2491060"
% 3.26/1.43 % (2491068)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1680905647:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.26/1.43 % (2491070)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=451128607:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.26/1.43 % (2491070)Also succeeded, but the first one will report.
% 3.26/1.43 % (2491068)Also succeeded, but the first one will report.
% 3.26/1.43 % (2491067)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=3321324806:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.26/1.43 % (2491066)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=1671434208:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.26/1.43 % (2491065)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=419802754:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.26/1.43 % (2491071)dis-21_1_sil=8000:lcm=predicate:random_seed=1959842082: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)
% 3.26/1.43 % (2491071)Also succeeded, but the first one will report.
% 3.26/1.43 % (2491069)Refutation found. Thanks to Tanya!
% 3.26/1.43 % SZS status Theorem for theBenchmark
% 3.26/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.26/1.43 % (2491069)------------------------------
% 3.26/1.43 % (2491069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.43 % (2491069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.43 % (2491069)CaDiCaL version: 2.1.3
% 3.26/1.43 % (2491069)Termination reason: Refutation
% 3.26/1.43 % (2491069)Time elapsed: 0.002 s
% 3.26/1.43 % (2491069)Peak memory usage: 88 MB
% 3.26/1.43 % (2491069)Instructions burned: 2 (million)
% 3.26/1.43 % (2491069)------------------------------
% 3.26/1.43 % (2491069)------------------------------
% 3.26/1.43 % (2491060)Success in time 0.378 s
% 3.26/1.43 % Vampire exiting
%------------------------------------------------------------------------------