%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO237+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 01:17:40 PM UTC 2026
% Result : Theorem 2.66s 0.77s
% Output : Proof 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 23 ~; 18 |; 14 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 36 ( 2 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,L] :
( apart_point_and_line(A,L)
<=> ( right_apart_point(A,L)
| left_apart_point(A,L) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_defns) ).
fof(f5_nnf,plain,
! [A,L] :
( ( ( ~ right_apart_point(A,L)
& ~ left_apart_point(A,L) )
| apart_point_and_line(A,L) )
& ( right_apart_point(A,L)
| left_apart_point(A,L)
| ~ apart_point_and_line(A,L) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,L] :
( ( ( ~ right_apart_point(A,L)
& ~ left_apart_point(A,L) )
| apart_point_and_line(A,L) )
& ( right_apart_point(A,L)
| left_apart_point(A,L)
| ~ apart_point_and_line(A,L) ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c10,plain,
( right_apart_point(X0,X1)
| left_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f36,conjecture,
! [A,B,C,L] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,B,C)
| divides_points(L,A,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [A,B,C,L] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,B,C)
| divides_points(L,A,C) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [A,B,C,L] :
( ~ divides_points(L,B,C)
& ~ divides_points(L,A,C)
& divides_points(L,A,B)
& apart_point_and_line(C,L) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ~ divides_points(sk3,sk1,sk2)
& ~ divides_points(sk3,sk0,sk2)
& divides_points(sk3,sk0,sk1)
& apart_point_and_line(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f36_nnf]) ).
cnf(c66,plain,
apart_point_and_line(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p83,plain,
( right_apart_point(sk2,sk3)
| left_apart_point(sk2,sk3) ),
inference(resolution,[status(thm)],[c10,c66]) ).
fof(f19,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_basics) ).
fof(f19_nnf,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c45,plain,
~ left_apart_point(X0,X1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p84,plain,
right_apart_point(sk2,sk3),
inference(resolution,[status(thm)],[p83,c45]) ).
fof(f1,axiom,
! [X,Y] :
( right_apart_point(X,Y)
<=> left_apart_point(X,reverse_line(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_defns) ).
fof(f1_nnf,plain,
! [X,Y] :
( ( ~ left_apart_point(X,reverse_line(Y))
| right_apart_point(X,Y) )
& ( left_apart_point(X,reverse_line(Y))
| ~ right_apart_point(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( ( ~ left_apart_point(X,reverse_line(Y))
| right_apart_point(X,Y) )
& ( left_apart_point(X,reverse_line(Y))
| ~ right_apart_point(X,Y) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( left_apart_point(X0,reverse_line(X1))
| ~ right_apart_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p85,plain,
left_apart_point(sk2,reverse_line(sk3)),
inference(resolution,[status(thm)],[p84,c2]) ).
cnf(p86,plain,
$false,
inference(resolution,[status(thm)],[p85,c45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO237+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 11:36:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.66/0.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.66/0.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------