%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO176+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 01:17:16 PM UTC 2026
% Result : Theorem 4.40s 1.20s
% Output : Proof 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 49 ( 16 ~; 17 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 17 !; 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/sandbox2/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(f12,conjecture,
! [X,Y,U,V] :
( ( ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_points(X,intersection_point(U,V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f12_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_points(X,intersection_point(U,V)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [X,Y,U,V] :
( ~ distinct_points(X,intersection_point(U,V))
& ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( ~ distinct_points(sk0,intersection_point(sk2,sk3))
& ( apart_point_and_line(sk0,sk3)
| apart_point_and_line(sk0,sk2) )
& convergent_lines(sk2,sk3)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f12_nnf]) ).
cnf(c15,plain,
convergent_lines(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p63,plain,
( distinct_points(X0,intersection_point(sk2,sk3))
| ~ apart_point_and_line(X0,sk3) ),
inference(resolution,[status(thm)],[c9,c15]) ).
cnf(c16,plain,
( apart_point_and_line(sk0,sk3)
| apart_point_and_line(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p66,plain,
( apart_point_and_line(sk0,sk2)
| distinct_points(sk0,intersection_point(sk2,sk3)) ),
inference(resolution,[status(thm)],[p63,c16]) ).
cnf(c17,plain,
~ distinct_points(sk0,intersection_point(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p68,plain,
apart_point_and_line(sk0,sk2),
inference(resolution,[status(thm)],[p66,c17]) ).
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(p46,plain,
( distinct_points(X0,intersection_point(sk2,sk3))
| ~ apart_point_and_line(X0,sk2) ),
inference(resolution,[status(thm)],[c8,c15]) ).
cnf(p71,plain,
distinct_points(sk0,intersection_point(sk2,sk3)),
inference(resolution,[status(thm)],[p68,p46]) ).
cnf(p81,plain,
$false,
inference(resolution,[status(thm)],[p71,c17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO176+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 11:17:44 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.40/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.40/1.20 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------