%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO208+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 : 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 09:54:01 AM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 61 ( 15 unt; 0 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 191 ( 75 ~; 83 |; 19 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 150 ( 144 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con1) ).
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(f9,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/sandbox/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(f10,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq2) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f14,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f15,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ convergent_lines(X1,X2) )
=> ~ distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ convergent_lines(X1,X2) )
=> ~ distinct_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f21,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f26,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(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(flattening,[],[f26]) ).
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(ennf_transformation,[],[f9]) ).
fof(f29,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,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f35,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f36,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
? [X0,X1,X2] :
( distinct_lines(X1,X2)
& ~ apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f38,plain,
? [X0,X1,X2] :
( distinct_lines(X1,X2)
& ~ apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
( distinct_lines(sK1,sK2)
& ~ apart_point_and_line(sK0,sK1)
& ~ apart_point_and_line(sK0,sK2)
& ~ convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f38]) ).
fof(f40,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f43,plain,
! [X2,X0,X1] :
( distinct_points(X0,X1)
| distinct_points(X2,X1)
| ~ distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| distinct_lines(X2,X1)
| ~ distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(X2,X1)
| ~ convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X2,X0,X1] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X2,X0,X1] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2)
| ~ distinct_points(X0,X3)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X2,X0,X1] :
( distinct_points(X0,X1)
| apart_point_and_line(X1,X2)
| ~ apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f52,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X2,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f13]) ).
fof(f55,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f56,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
~ convergent_lines(sK1,sK2),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
~ apart_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f39]) ).
fof(f79,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f40,f41,f42,f43,f44,f45,f47,f46,f49,f48,f50,f51,f52,f53,f54,f55,f56,f60,f59,f58,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO208+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 07:37:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 Running first-order model finding
% 0.14/0.40 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
% 0.14/0.45 % (2768163)Will run a generic schedule for satisfiability detection.
% 0.14/0.45 % (2768168)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1291087327_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.45 % TRYING [1]
% 0.14/0.45 % TRYING [2]
% 0.14/0.45 % (2768168) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2768163-2768168"...
% 0.14/0.45 % (2768168)...printing done.
% 0.14/0.45 % (2768168)Refutation found. Thanks to Tanya!
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (2768168)------------------------------
% 0.14/0.45 % (2768168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (2768168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (2768168)CaDiCaL version: 2.1.3
% 0.14/0.45 % (2768168)Termination reason: Refutation
% 0.14/0.45 % (2768168)Time elapsed: 0.002 s
% 0.14/0.45 % (2768168)Peak memory usage: 11 MB
% 0.14/0.45 % (2768168)Instructions burned: 3 (million)
% 0.14/0.45 % (2768163)Success in time 0.036 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------