%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO265+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 01:17:47 PM UTC 2026
% Result : Theorem 3.27s 0.83s
% Output : Proof 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 50 ( 22 ~; 15 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 0-1 aty)
% Number of variables : 30 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5_defns) ).
fof(f4_nnf,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c9,plain,
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f36,conjecture,
! [L,M] :
( equally_directed_lines(L,reverse_line(M))
=> equally_directed_opposite_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [L,M] :
( equally_directed_lines(L,reverse_line(M))
=> equally_directed_opposite_lines(L,M) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [L,M] :
( ~ equally_directed_opposite_lines(L,M)
& equally_directed_lines(L,reverse_line(M)) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ~ equally_directed_opposite_lines(sk0,sk1)
& equally_directed_lines(sk0,reverse_line(sk1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f36_nnf]) ).
cnf(c67,plain,
~ equally_directed_opposite_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p71,plain,
unequally_directed_opposite_lines(sk0,sk1),
inference(resolution,[status(thm)],[c9,c67]) ).
fof(f0,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1_defns) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p72,plain,
unequally_directed_lines(sk0,reverse_line(sk1)),
inference(resolution,[status(thm)],[p71,c0]) ).
fof(f3,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4_defns) ).
fof(f3_nnf,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c6,plain,
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c66,plain,
equally_directed_lines(sk0,reverse_line(sk1)),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p69,plain,
~ unequally_directed_lines(sk0,reverse_line(sk1)),
inference(resolution,[status(thm)],[c6,c66]) ).
cnf(p73,plain,
$false,
inference(resolution,[status(thm)],[p72,p69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO265+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n004.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 11:45:50 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.27/0.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.27/0.83 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------