%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO170+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:17:14 PM UTC 2026
% Result : Theorem 5.36s 1.12s
% Output : Proof 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 86 ( 36 ~; 34 |; 11 &)
% ( 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 : 43 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,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/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f10_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)],[f10]) ).
fof(f10_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)],[f10_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)],[f10_sk]) ).
fof(f14,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/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14_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)],[f14]) ).
fof(f14_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)],[f14_neg]) ).
fof(f14_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])],[f14_nnf]) ).
cnf(c14,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p26,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)],[f14_sk]) ).
cnf(p68,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)],[p26,c17]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p23,plain,
~ apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(resolution,[status(thm)],[c7,c14]) ).
cnf(p472,plain,
( 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)],[p68,p23]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p21,plain,
~ apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(resolution,[status(thm)],[c6,c14]) ).
cnf(p473,plain,
( apart_point_and_line(sk1,sk2)
| apart_point_and_line(sk0,sk2) ),
inference(resolution,[status(thm)],[p472,p21]) ).
cnf(c16,plain,
~ apart_point_and_line(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p474,plain,
apart_point_and_line(sk0,sk2),
inference(resolution,[status(thm)],[p473,c16]) ).
cnf(c15,plain,
~ apart_point_and_line(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p475,plain,
$false,
inference(resolution,[status(thm)],[p474,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO170+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 11:15:03 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.36/1.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.36/1.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------