%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO215+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 : n005.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 01:17:33 PM UTC 2026
% Result : Theorem 7.18s 1.50s
% Output : Proof 7.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 79 ( 29 ~; 38 |; 6 &)
% ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
fof(f19_nnf,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [L,M,A,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c24,plain,
( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f11,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f11_nnf,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c13,plain,
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f20,conjecture,
! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f20_neg,negated_conjecture,
~ ! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ unorthogonal_lines(L,N)
& convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( ~ unorthogonal_lines(sk1,sk2)
& ~ unorthogonal_lines(sk0,sk2)
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f20_nnf]) ).
cnf(c25,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p28,plain,
distinct_lines(sk0,sk1),
inference(resolution,[status(thm)],[c13,c25]) ).
cnf(p326,plain,
( unorthogonal_lines(sk1,X1)
| unorthogonal_lines(sk0,X1)
| apart_point_and_line(X0,sk1)
| apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[c24,p28]) ).
cnf(c27,plain,
~ unorthogonal_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p4872,plain,
( unorthogonal_lines(sk0,sk2)
| apart_point_and_line(X0,sk1)
| apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[p326,c27]) ).
cnf(c26,plain,
~ unorthogonal_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p4922,plain,
( apart_point_and_line(X0,sk1)
| apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[p4872,c26]) ).
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]) ).
cnf(p75,plain,
( distinct_points(X0,intersection_point(sk0,sk1))
| ~ apart_point_and_line(X0,sk1) ),
inference(resolution,[status(thm)],[c9,c25]) ).
cnf(p4923,plain,
( distinct_points(X0,intersection_point(sk0,sk1))
| apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[p4922,p75]) ).
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(p4956,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(resolution,[status(thm)],[p4923,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(p57,plain,
( distinct_points(X0,intersection_point(sk0,sk1))
| ~ apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[c8,c25]) ).
cnf(p4961,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)),
inference(resolution,[status(thm)],[p4956,p57]) ).
cnf(p4997,plain,
$false,
inference(resolution,[status(thm)],[p4961,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO215+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.41 % Computer : n005.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Wed Sep 23 11:31:32 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.18/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.18/1.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------