%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 : Fri Sep 25 01:17:37 PM UTC 2026
% Result : Theorem 0.14s 5.79s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 21 ~; 15 |; 16 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 33 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
fof(f7_nnf,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f16,conjecture,
! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( ~ apart_point_and_line(X,M)
& ~ apart_point_and_line(X,L) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16_neg,negated_conjecture,
~ ! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( ~ apart_point_and_line(X,M)
& ~ apart_point_and_line(X,L) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [L,M] :
( ! [X] :
( ( apart_point_and_line(X,M)
| apart_point_and_line(X,L) )
& point(X) )
& convergent_lines(L,M)
& line(M)
& line(L) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
! [X] :
( ( apart_point_and_line(X,sk1)
| apart_point_and_line(X,sk0) )
& point(X)
& convergent_lines(sk0,sk1)
& line(sk1)
& line(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f16_nnf]) ).
cnf(c20,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p76,plain,
( distinct_points(X0,intersection_point(sk0,sk1))
| ~ apart_point_and_line(X0,sk1) ),
inference(resolution,[status(thm)],[c9,c20]) ).
cnf(c22,plain,
( apart_point_and_line(X2,sk1)
| apart_point_and_line(X2,sk0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p93,plain,
( apart_point_and_line(X0,sk0)
| distinct_points(X0,intersection_point(sk0,sk1)) ),
inference(resolution,[status(thm)],[p76,c22]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p94,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(resolution,[status(thm)],[p93,c0]) ).
cnf(c8,plain,
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p58,plain,
( distinct_points(X0,intersection_point(sk0,sk1))
| ~ apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[c8,c20]) ).
cnf(p99,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)),
inference(resolution,[status(thm)],[p94,p58]) ).
cnf(p100,plain,
$false,
inference(resolution,[status(thm)],[p99,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n011.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 11:34:32 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/5.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------