%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO238+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 : n003.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 4.28s 1.08s
% Output : Proof 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 69 ( 25 ~; 20 |; 20 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 40 ( 3 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,L] :
( divides_points(L,A,B)
<=> ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8_defns) ).
fof(f7_nnf,plain,
! [A,B,L] :
( ( ( ( ~ left_apart_point(B,L)
| ~ right_apart_point(A,L) )
& ( ~ right_apart_point(B,L)
| ~ left_apart_point(A,L) ) )
| divides_points(L,A,B) )
& ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [L,A,B] :
( ( ( ( ~ left_apart_point(B,L)
| ~ right_apart_point(A,L) )
& ( ~ right_apart_point(B,L)
| ~ left_apart_point(A,L) ) )
| divides_points(L,A,B) )
& ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c16,plain,
( right_apart_point(X0,X2)
| left_apart_point(X0,X2)
| ~ divides_points(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f36,conjecture,
! [A,B,C,L] :
( ( divides_points(L,A,C)
& divides_points(L,A,B) )
=> ~ divides_points(L,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [A,B,C,L] :
( ( divides_points(L,A,C)
& divides_points(L,A,B) )
=> ~ divides_points(L,B,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) ),
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) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f36_nnf]) ).
cnf(c68,plain,
divides_points(sk3,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p86,plain,
( right_apart_point(sk1,sk3)
| left_apart_point(sk1,sk3) ),
inference(resolution,[status(thm)],[c16,c68]) ).
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(p88,plain,
right_apart_point(sk1,sk3),
inference(resolution,[status(thm)],[p86,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(p89,plain,
left_apart_point(sk1,reverse_line(sk3)),
inference(resolution,[status(thm)],[p88,c2]) ).
cnf(p91,plain,
$false,
inference(resolution,[status(thm)],[p89,c45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO238+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n003.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 11:39:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.28/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.28/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------