%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO245+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 01:17:42 PM UTC 2026
% Result : Theorem 3.36s 0.89s
% Output : Proof 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 3 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 20 ( 9 ~; 1 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 2 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(f36,conjecture,
! [A,B,C] :
( distinct_points(A,B)
=> ( left_apart_point(C,line_connecting(A,B))
=> right_apart_point(B,line_connecting(A,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [A,B,C] :
( distinct_points(A,B)
=> ( left_apart_point(C,line_connecting(A,B))
=> right_apart_point(B,line_connecting(A,C)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [A,B,C] :
( ~ right_apart_point(B,line_connecting(A,C))
& left_apart_point(C,line_connecting(A,B))
& distinct_points(A,B) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ~ right_apart_point(sk1,line_connecting(sk0,sk2))
& left_apart_point(sk2,line_connecting(sk0,sk1))
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f36_nnf]) ).
cnf(c67,plain,
left_apart_point(sk2,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p69,plain,
$false,
inference(resolution,[status(thm)],[c45,c67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO245+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 11:39:20 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.36/0.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.36/0.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------