%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO185+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 : n007.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 09:51:51 AM UTC 2026
% Result : Theorem 3.42s 1.42s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 9 unt; 2 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 77 ( 34 ~; 20 |; 17 &)
% ( 2 <=>; 4 =>; 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 : 31 ( 0 sgn 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)
& ~ distinct_points(X0,intersection_point(X2,X3)) )
=> ( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,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)
& ~ distinct_points(X0,intersection_point(X2,X3)) )
=> ( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3) )
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ distinct_points(X0,intersection_point(X2,X3)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3) )
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ distinct_points(X0,intersection_point(X2,X3)) ),
inference(flattening,[],[f16]) ).
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(ennf_transformation,[],[f8]) ).
fof(f21,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,[],[f20]) ).
fof(f26,plain,
( ( apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,sK3) )
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& ~ distinct_points(sK0,intersection_point(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17]) ).
fof(f27,plain,
~ distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f26]) ).
fof(f28,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f30,plain,
( apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,sK3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f33,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,definition,
( spl4_1
<=> apart_point_and_line(sK0,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f43,definition,
( spl4_2
<=> apart_point_and_line(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f45,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f30,f43,f39]) ).
fof(f50,plain,
( ~ apart_point_and_line(sK0,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f27,f33]) ).
fof(f51,plain,
( ~ apart_point_and_line(sK0,sK2)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f27,f34]) ).
fof(f52,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f51,f45]) ).
fof(f53,plain,
~ apart_point_and_line(sK0,sK3),
inference(forward_subsumption_resolution,[],[f50,f28]) ).
fof(f54,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f52,f28]) ).
fof(f55,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f54]) ).
fof(f56,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f53,f39]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO185+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 07:25:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.42/1.42 % (1072988)Detected formulas, will run a generic FOF schedule.
% 3.42/1.42 % (1073080)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=138646363:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.42/1.42 % (1073082)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=535330582:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.42/1.42 % (1073078)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=4216736570:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.42/1.42 % (1073081)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4190443784:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.42/1.42 % (1073079)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=1943271718:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.42/1.42 % (1073081)First to succeed.
% 3.42/1.42 % (1073082)Also succeeded, but the first one will report.
% 3.42/1.42 % (1073081)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1072988"
% 3.42/1.42 % (1073084)dis-21_1_sil=8000:lcm=predicate:random_seed=1247944505: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)
% 3.42/1.42 % (1073084)Also succeeded, but the first one will report.
% 3.42/1.42 % (1073083)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=856616685:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.42/1.42 % (1073083)Also succeeded, but the first one will report.
% 3.42/1.42 % (1073081)Refutation found. Thanks to Tanya!
% 3.42/1.42 % SZS status Theorem for theBenchmark
% 3.42/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.42 % (1073081)------------------------------
% 3.42/1.42 % (1073081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.42 % (1073081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.42 % (1073081)CaDiCaL version: 2.1.3
% 3.42/1.42 % (1073081)Termination reason: Refutation
% 3.42/1.42 % (1073081)Time elapsed: 0.002 s
% 3.42/1.42 % (1073081)Peak memory usage: 89 MB
% 3.42/1.42 % (1073081)Instructions burned: 1 (million)
% 3.42/1.42 % (1073081)------------------------------
% 3.42/1.42 % (1073081)------------------------------
% 3.42/1.42 % (1072988)Success in time 0.394 s
% 3.42/1.42 % Vampire exiting
%------------------------------------------------------------------------------