%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO232+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 : Thu Sep 24 12:24:39 PM UTC 2026
% Result : Theorem 0.09s 0.74s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 17 ~; 14 |; 4 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 34 ( 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [L] : equally_directed_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L] : unequally_directed_opposite_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L] : unequally_directed_opposite_lines(L,L),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,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)],[f1]) ).
fof(f40,plain,
( ! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ! [X,Y] :
( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f42,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f51,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)],[f4]) ).
fof(f52,plain,
( ! [X,Y] :
( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ! [X,Y] :
( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f100,plain,
! [X0] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f110,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f152,plain,
? [L] : ~ unequally_directed_opposite_lines(L,L),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
~ unequally_directed_opposite_lines(sK0_skl,sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(L,sK0_skl)],[f152]) ).
fof(f154,plain,
~ unequally_directed_opposite_lines(sK0_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f166,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f110,f42]) ).
fof(f169,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(resolution,[status(thm)],[f166,f53]) ).
fof(f173,plain,
! [X0] : unequally_directed_opposite_lines(X0,X0),
inference(resolution,[status(thm)],[f169,f100]) ).
fof(f175,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f154,f173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO232+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.70 % Computer : n006.cluster.edu
% 0.09/0.70 % Model : x86_64 x86_64
% 0.09/0.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.70 % Memory : 8046.5625MB
% 0.09/0.70 % OS : Linux 6.8.0-71-generic
% 0.09/0.71 % CPULimit : 300
% 0.09/0.71 % WCLimit : 300
% 0.09/0.71 % DateTime : Sun Sep 20 14:09:16 UTC 2026
% 0.09/0.71 % CPUTime :
% 0.09/0.72 % Drodi V4.1.1
% 0.09/0.74 % Refutation found
% 0.09/0.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.76 % Elapsed time: 0.046168 seconds
% 0.09/0.76 % CPU time: 0.118897 seconds
% 0.09/0.76 % Total memory used: 19.116 MB
% 0.09/0.76 % Net memory used: 19.036 MB
%------------------------------------------------------------------------------