%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO225+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 : 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 01:17:36 PM UTC 2026
% Result : Theorem 5.33s 1.71s
% Output : Proof 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 75 ( 22 ~; 29 |; 17 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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]) ).
fof(f3,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
fof(f3_nnf,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f16,conjecture,
! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16_neg,negated_conjecture,
~ ! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [A,B] :
( ! [X] :
( ( apart_point_and_line(B,X)
| apart_point_and_line(A,X) )
& line(X) )
& distinct_points(A,B)
& point(B)
& point(A) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
! [X] :
( ( apart_point_and_line(sk1,X)
| apart_point_and_line(sk0,X) )
& line(X)
& distinct_points(sk0,sk1)
& point(sk1)
& point(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f16_nnf]) ).
cnf(c20,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p23,plain,
( distinct_points(sk1,X0)
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[c3,c20]) ).
cnf(p24,plain,
( distinct_points(X0,X1)
| distinct_points(sk1,X1)
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[p23,c3]) ).
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(p25,plain,
( distinct_points(X0,sk1)
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[p24,c0]) ).
cnf(p29,plain,
( distinct_points(X0,X1)
| distinct_points(sk0,X1)
| distinct_points(X0,sk1) ),
inference(resolution,[status(thm)],[p25,c3]) ).
cnf(p30,plain,
( distinct_points(X0,sk0)
| distinct_points(X0,sk1) ),
inference(resolution,[status(thm)],[p29,c0]) ).
cnf(p33,plain,
distinct_points(sk1,sk0),
inference(resolution,[status(thm)],[p30,c0]) ).
cnf(p92,plain,
( distinct_points(X0,sk0)
| ~ apart_point_and_line(X0,line_connecting(sk1,sk0)) ),
inference(resolution,[status(thm)],[c7,p33]) ).
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(p59,plain,
( distinct_points(X0,sk1)
| ~ apart_point_and_line(X0,line_connecting(sk1,sk0)) ),
inference(resolution,[status(thm)],[c6,p33]) ).
cnf(c22,plain,
( apart_point_and_line(sk1,X2)
| apart_point_and_line(sk0,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p79,plain,
( apart_point_and_line(sk0,line_connecting(sk1,sk0))
| distinct_points(sk1,sk1) ),
inference(resolution,[status(thm)],[p59,c22]) ).
cnf(p113,plain,
( distinct_points(sk1,sk1)
| distinct_points(sk0,sk0) ),
inference(resolution,[status(thm)],[p92,p79]) ).
cnf(p114,plain,
distinct_points(sk0,sk0),
inference(resolution,[status(thm)],[p113,c0]) ).
cnf(p115,plain,
$false,
inference(resolution,[status(thm)],[p114,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.63 % Computer : n007.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.63 % CPULimit : 300
% 0.16/0.64 % WCLimit : 300
% 0.16/0.64 % DateTime : Wed Sep 23 11:32:23 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.16/0.64 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.33/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.33/1.71 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------