%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO176+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 : n019.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 3.75s 1.52s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 8 unt; 2 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 36 ~; 33 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
fof(f36,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(f37,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)],[f36]) ).
fof(f40,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,[],[f37]) ).
fof(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f43,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f42]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f50,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)],[f41]) ).
fof(f51,plain,
( apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,sK3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f52,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f50]) ).
fof(f54,plain,
~ distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f50]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f58,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,definition,
( spl4_1
<=> apart_point_and_line(sK0,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f65,plain,
( apart_point_and_line(sK0,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl4_2
<=> apart_point_and_line(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f69,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f51,f67,f63]) ).
fof(f73,plain,
( ! [X0] :
( apart_point_and_line(X0,sK2)
| distinct_points(sK0,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f69,f55]) ).
fof(f80,plain,
( ! [X0] :
( distinct_points(sK0,intersection_point(sK2,X0))
| ~ convergent_lines(sK2,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f73,f59]) ).
fof(f82,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_2 ),
inference(resolution,[],[f80,f54]) ).
fof(f84,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f82,f52]) ).
fof(f85,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f84]) ).
fof(f86,plain,
( ! [X0] :
( apart_point_and_line(X0,sK3)
| distinct_points(sK0,X0) )
| ~ spl4_1 ),
inference(resolution,[],[f65,f55]) ).
fof(f88,plain,
( ! [X0] :
( distinct_points(sK0,intersection_point(X0,sK3))
| ~ convergent_lines(X0,sK3) )
| ~ spl4_1 ),
inference(resolution,[],[f86,f58]) ).
fof(f90,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_1 ),
inference(resolution,[],[f88,f54]) ).
fof(f92,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f90,f52]) ).
fof(f93,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f92]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f70]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f85]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f93]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f94,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO176+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n019.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 07:24:34 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 3.75/1.52 % (2762293)Detected formulas, will run a generic FOF schedule.
% 3.75/1.52 % (2762298)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=445433620:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.75/1.52 % (2762299)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=711090733:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.75/1.52 % (2762302)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1956642364:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.75/1.52 % (2762304)dis-21_1_sil=8000:lcm=predicate:random_seed=1927219680: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)
% 3.75/1.52 % (2762301)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1483318295:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.75/1.52 % (2762303)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=806173869:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.75/1.52 % (2762300)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=3413495665:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.75/1.52 % (2762304)Also succeeded, but the first one will report.
% 3.75/1.52 % (2762301)First to succeed.
% 3.75/1.52 % (2762302)Also succeeded, but the first one will report.
% 3.75/1.52 % (2762301)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2762293"
% 3.75/1.52 % (2762303)Also succeeded, but the first one will report.
% 3.75/1.52 % (2762301)Refutation found. Thanks to Tanya!
% 3.75/1.52 % SZS status Theorem for theBenchmark
% 3.75/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.52 % (2762301)------------------------------
% 3.75/1.52 % (2762301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.52 % (2762301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.52 % (2762301)CaDiCaL version: 2.1.3
% 3.75/1.52 % (2762301)Termination reason: Refutation
% 3.75/1.52 % (2762301)Time elapsed: 0.003 s
% 3.75/1.52 % (2762301)Peak memory usage: 89 MB
% 3.75/1.52 % (2762301)Instructions burned: 2 (million)
% 3.75/1.52 % (2762301)------------------------------
% 3.75/1.52 % (2762301)------------------------------
% 3.75/1.52 % (2762293)Success in time 0.437 s
% 3.75/1.52 % Vampire exiting
%------------------------------------------------------------------------------