%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO185+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 : 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 09:53:51 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% 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 : 95 ( 42 ~; 31 |; 15 &)
% ( 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/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(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/Axioms/GEO006+0.ax',ceq1) ).
fof(f15,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/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,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)],[f15]) ).
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(f29,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(f30,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f35,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,[],[f16]) ).
fof(f36,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,[],[f35]) ).
fof(f37,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)],[f36]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
~ distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
( apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,sK3) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,definition,
( spl4_1
<=> apart_point_and_line(sK0,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f59,plain,
( apart_point_and_line(sK0,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl4_2
<=> apart_point_and_line(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f63,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f55,f61,f57]) ).
fof(f77,plain,
( ! [X0] :
( apart_point_and_line(X0,sK2)
| distinct_points(sK0,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f49,f63]) ).
fof(f78,plain,
( ! [X0] :
( distinct_points(sK0,intersection_point(sK2,X0))
| ~ convergent_lines(sK2,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f77,f46]) ).
fof(f94,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_2 ),
inference(resolution,[],[f78,f52]) ).
fof(f96,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f94,f53]) ).
fof(f97,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f99,plain,
( ! [X0] :
( apart_point_and_line(X0,sK3)
| distinct_points(sK0,X0) )
| ~ spl4_1 ),
inference(resolution,[],[f59,f49]) ).
fof(f106,plain,
( ! [X0] :
( distinct_points(sK0,intersection_point(X0,sK3))
| ~ convergent_lines(X0,sK3) )
| ~ spl4_1 ),
inference(resolution,[],[f99,f47]) ).
fof(f122,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_1 ),
inference(resolution,[],[f106,f52]) ).
fof(f124,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f122,f53]) ).
fof(f125,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f124]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f97]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f125]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f126,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO185+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n007.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 07:25:55 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.17/0.48 % (1072866)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (1072887)dis+10_1_sil=32000:sp=arity:random_seed=3868436749:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (1072887) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1072866-1072887"...
% 0.17/0.48 % (1072887)...printing done.
% 0.17/0.48 % (1072887)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (1072887)------------------------------
% 0.17/0.48 % (1072887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1072887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1072887)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1072887)Termination reason: Refutation
% 0.17/0.48 % (1072887)Time elapsed: 0.002 s
% 0.17/0.48 % (1072887)Peak memory usage: 12 MB
% 0.17/0.48 % (1072887)Instructions burned: 3 (million)
% 0.17/0.48 % (1072866)Success in time 0.039 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------