%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 09:54:08 AM UTC 2026
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 68 ( 25 ~; 17 |; 20 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
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/Axioms/GEO008+0.ax',con2) ).
fof(f17,conjecture,
! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> ? [X2] :
( point(X2)
=> ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> ? [X2] :
( point(X2)
=> ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f44,plain,
? [X0,X1] :
( ! [X2] :
( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
& point(X2) )
& line(X0)
& line(X1)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f45,plain,
? [X0,X1] :
( ! [X2] :
( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
& point(X2) )
& line(X0)
& line(X1)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ! [X2] :
( ( apart_point_and_line(X2,sK0)
| apart_point_and_line(X2,sK1) )
& point(X2) )
& line(sK0)
& line(sK1)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f45]) ).
fof(f47,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f55,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f65,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
! [X2] :
( apart_point_and_line(X2,sK1)
| apart_point_and_line(X2,sK0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f99,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f55,f47]) ).
fof(f110,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f56,f47]) ).
fof(f134,plain,
! [X0] :
( apart_point_and_line(intersection_point(X0,sK1),sK0)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f99,f69]) ).
fof(f140,plain,
( ~ convergent_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f110,f134]) ).
fof(f146,plain,
~ convergent_lines(sK0,sK1),
inference(duplicate_literal_removal,[],[f140]) ).
fof(f147,plain,
$false,
inference(forward_subsumption_resolution,[],[f146,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 07:45:52 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 % (3180549)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (3180557)dis+10_1_sil=32000:sp=arity:random_seed=366602252:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.46 % (3180557) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3180549-3180557"...
% 0.18/0.46 % (3180557)...printing done.
% 0.18/0.46 % (3180555)% WARNING: option uhcvi not known.
% 0.18/0.46 % (3180557)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Theorem for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (3180557)------------------------------
% 0.18/0.46 % (3180557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.46 % (3180557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.46 % (3180557)CaDiCaL version: 2.1.3
% 0.18/0.46 % (3180557)Termination reason: Refutation
% 0.18/0.46 % (3180557)Time elapsed: 0.002 s
% 0.18/0.46 % (3180557)Peak memory usage: 11 MB
% 0.18/0.46 % (3180557)Instructions burned: 3 (million)
% 0.18/0.46 % (3180549)Success in time 0.029 s
% 0.18/0.46 % Vampire exiting
%------------------------------------------------------------------------------