%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO172+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 09:53:46 AM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 12 unt; 2 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 142 ( 52 ~; 70 |; 11 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 72 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',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/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,conjecture,
! [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/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [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)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
& convergent_lines(X0,X1)
& ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
& convergent_lines(X0,X1)
& ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
~ apart_point_and_line(sK2,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
~ apart_point_and_line(sK2,sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f53,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
distinct_points(sK2,intersection_point(sK0,sK1)),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f42,f53]) ).
fof(f58,plain,
! [X0,X1] :
( convergent_lines(sK0,X0)
| convergent_lines(X0,X1)
| convergent_lines(sK1,X1) ),
inference(resolution,[],[f56,f42]) ).
fof(f59,plain,
! [X0] :
( distinct_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f50,f53]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,sK1)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,sK1)
| convergent_lines(sK0,X2) ),
inference(resolution,[],[f47,f59]) ).
fof(f71,plain,
! [X0] :
( convergent_lines(sK0,X0)
| convergent_lines(X0,sK1) ),
inference(resolution,[],[f58,f39]) ).
fof(f91,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK2,sK1)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f63,f54]) ).
fof(f97,definition,
( spl3_1
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f99,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f109,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(sK2,X0)
| convergent_lines(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f91,f51]) ).
fof(f111,definition,
( spl3_4
<=> ! [X0] :
( apart_point_and_line(intersection_point(sK0,sK1),X0)
| convergent_lines(sK0,X0)
| apart_point_and_line(sK2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f112,plain,
( ! [X0] :
( apart_point_and_line(intersection_point(sK0,sK1),X0)
| convergent_lines(sK0,X0)
| apart_point_and_line(sK2,X0) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( spl3_1
| spl3_4 ),
inference(avatar_split_clause,[],[f109,f111,f97]) ).
fof(f126,plain,
( convergent_lines(sK0,sK0)
| apart_point_and_line(sK2,sK0)
| ~ convergent_lines(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f112,f45]) ).
fof(f132,plain,
( convergent_lines(sK0,sK0)
| apart_point_and_line(sK2,sK0)
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f126,f71]) ).
fof(f133,plain,
( apart_point_and_line(sK2,sK0)
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f132,f39]) ).
fof(f134,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f133,f52]) ).
fof(f135,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f136,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_1 ),
inference(resolution,[],[f99,f46]) ).
fof(f139,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f136,f53]) ).
fof(f140,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f139]) ).
cnf(s3,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f113]) ).
cnf(s5,plain,
~ spl3_4,
inference(sat_conversion,[],[f135]) ).
cnf(s6,plain,
~ spl3_1,
inference(sat_conversion,[],[f140]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s3,s5,s6]) ).
fof(f141,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO172+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 07:27:45 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.46 % (3220683)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (3220689)% WARNING: option uhcvi not known.
% 0.13/0.46 % (3220689)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2018157741:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.46 % (3220689) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3220683-3220689"...
% 0.13/0.46 % (3220689)...printing done.
% 0.13/0.46 % (3220689)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (3220689)------------------------------
% 0.13/0.46 % (3220689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (3220689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (3220689)CaDiCaL version: 2.1.3
% 0.13/0.46 % (3220689)Termination reason: Refutation
% 0.13/0.46 % (3220689)Time elapsed: 0.002 s
% 0.13/0.46 % (3220689)Peak memory usage: 12 MB
% 0.13/0.46 % (3220689)Instructions burned: 4 (million)
% 0.13/0.46 % (3220683)Success in time 0.027 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------