%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO170+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 : n007.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 01:17:14 PM UTC 2026
% Result : Theorem 5.44s 1.33s
% Output : Proof 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 97 ( 34 ~; 44 |; 14 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f8_nnf,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f12,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Y,Z)
& ~ apart_point_and_line(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_lines(Z,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f12_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(Y,Z)
& ~ apart_point_and_line(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_lines(Z,line_connecting(X,Y)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [X,Y,Z] :
( distinct_lines(Z,line_connecting(X,Y))
& ~ apart_point_and_line(Y,Z)
& ~ apart_point_and_line(X,Z)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( distinct_lines(sk2,line_connecting(sk0,sk1))
& ~ apart_point_and_line(sk1,sk2)
& ~ apart_point_and_line(sk0,sk2)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f12_nnf]) ).
cnf(c14,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p81,plain,
( apart_point_and_line(sk1,X1)
| apart_point_and_line(sk1,X0)
| apart_point_and_line(sk0,X1)
| apart_point_and_line(sk0,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[c10,c14]) ).
cnf(c17,plain,
distinct_lines(sk2,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p304,plain,
( apart_point_and_line(sk1,line_connecting(sk0,sk1))
| apart_point_and_line(sk1,sk2)
| apart_point_and_line(sk0,line_connecting(sk0,sk1))
| apart_point_and_line(sk0,sk2) ),
inference(resolution,[status(thm)],[p81,c17]) ).
fof(f6,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).
fof(f6_nnf,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c7,plain,
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p34,plain,
( distinct_points(X0,sk1)
| ~ apart_point_and_line(X0,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[c7,c14]) ).
cnf(p1320,plain,
( distinct_points(sk1,sk1)
| apart_point_and_line(sk1,sk2)
| apart_point_and_line(sk0,line_connecting(sk0,sk1))
| apart_point_and_line(sk0,sk2) ),
inference(resolution,[status(thm)],[p304,p34]) ).
cnf(c6,plain,
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p22,plain,
( distinct_points(X0,sk0)
| ~ apart_point_and_line(X0,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[c6,c14]) ).
cnf(p1322,plain,
( distinct_points(sk0,sk0)
| distinct_points(sk1,sk1)
| apart_point_and_line(sk1,sk2)
| apart_point_and_line(sk0,sk2) ),
inference(resolution,[status(thm)],[p1320,p22]) ).
cnf(c16,plain,
~ apart_point_and_line(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p1324,plain,
( distinct_points(sk0,sk0)
| distinct_points(sk1,sk1)
| apart_point_and_line(sk0,sk2) ),
inference(resolution,[status(thm)],[p1322,c16]) ).
cnf(c15,plain,
~ apart_point_and_line(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p1325,plain,
( distinct_points(sk0,sk0)
| distinct_points(sk1,sk1) ),
inference(resolution,[status(thm)],[p1324,c15]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/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(p1326,plain,
distinct_points(sk0,sk0),
inference(resolution,[status(thm)],[p1325,c0]) ).
cnf(p1328,plain,
$false,
inference(resolution,[status(thm)],[p1326,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO170+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 11:12:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.44/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.44/1.33 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------