%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO233+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 27 ~; 20 |; 5 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 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 : 46 ( 45 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [L] : equally_directed_lines(L,L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L] : equally_directed_lines(reverse_line(reverse_line(L)),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L] : equally_directed_lines(reverse_line(reverse_line(L)),L),
inference(negated_conjecture,[status(cth)],[f37]) ).
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(f54,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(f111,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f112,plain,
! [X0,X1] :
( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f117,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f118,plain,
( ! [L,M] : ~ left_convergent_lines(L,reverse_line(M))
& ! [L,M] : ~ left_convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f152,plain,
? [L] : ~ equally_directed_lines(reverse_line(reverse_line(L)),L),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
~ equally_directed_lines(reverse_line(reverse_line(sK0_skl)),sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(L,sK0_skl)],[f152]) ).
fof(f154,plain,
~ equally_directed_lines(reverse_line(reverse_line(sK0_skl)),sK0_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f165,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f112,f119]) ).
fof(f171,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f119]) ).
fof(f173,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f110,f53]) ).
fof(f174,plain,
! [X0] : unequally_directed_lines(reverse_line(X0),X0),
inference(resolution,[status(thm)],[f173,f100]) ).
fof(f198,plain,
! [X0] : ~ unequally_directed_lines(reverse_line(reverse_line(X0)),X0),
inference(resolution,[status(thm)],[f171,f174]) ).
fof(f202,plain,
! [X0] : equally_directed_lines(reverse_line(reverse_line(X0)),X0),
inference(resolution,[status(thm)],[f198,f54]) ).
fof(f204,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f154,f202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO233+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 14:14:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.064372 seconds
% 0.09/0.44 % CPU time: 0.263066 seconds
% 0.09/0.44 % Total memory used: 20.881 MB
% 0.09/0.44 % Net memory used: 20.473 MB
%------------------------------------------------------------------------------