%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO233+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 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 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 26 ~; 30 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 56 ( 55 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,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(f16,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,L] : ~ unequally_directed_lines(parallel_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [L] : ~ unequally_directed_lines(reverse_line(reverse_line(L)),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [L] : ~ unequally_directed_lines(reverse_line(reverse_line(L)),L),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f78,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f79,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f80,plain,
! [L,M] :
( ! [N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) )
| ~ unequally_directed_lines(L,M) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f90,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)],[f14]) ).
fof(f91,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)],[f90]) ).
fof(f96,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f97,plain,
( ! [L,M] : ~ left_convergent_lines(L,reverse_line(M))
& ! [L,M] : ~ left_convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f117,plain,
! [X0,X1] : ~ unequally_directed_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f130,plain,
? [L] : unequally_directed_lines(reverse_line(reverse_line(L)),L),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
unequally_directed_lines(reverse_line(reverse_line(sK0_skl)),sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(L,sK0_skl)],[f130]) ).
fof(f132,plain,
unequally_directed_lines(reverse_line(reverse_line(sK0_skl)),sK0_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f144,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)],[f91,f98]) ).
fof(f149,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f98]) ).
fof(f150,plain,
! [X0] :
( unequally_directed_lines(sK0_skl,X0)
| unequally_directed_lines(reverse_line(reverse_line(sK0_skl)),X0) ),
inference(resolution,[status(thm)],[f81,f132]) ).
fof(f151,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(reverse_line(reverse_line(sK0_skl)),X1)
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f150,f81]) ).
fof(f155,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(sK0_skl,X2)
| unequally_directed_lines(X1,X0)
| unequally_directed_lines(reverse_line(reverse_line(sK0_skl)),X0) ),
inference(resolution,[status(thm)],[f151,f81]) ).
fof(f161,plain,
! [X0] :
( unequally_directed_lines(X0,reverse_line(reverse_line(sK0_skl)))
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f151,f78]) ).
fof(f183,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(sK0_skl,X1)
| unequally_directed_lines(X0,reverse_line(reverse_line(sK0_skl))) ),
inference(resolution,[status(thm)],[f155,f78]) ).
fof(f208,plain,
! [X0] :
( unequally_directed_lines(X0,sK0_skl)
| unequally_directed_lines(X0,reverse_line(reverse_line(sK0_skl))) ),
inference(resolution,[status(thm)],[f183,f78]) ).
fof(f244,plain,
! [X0] : unequally_directed_lines(sK0_skl,parallel_through_point(reverse_line(reverse_line(sK0_skl)),X0)),
inference(resolution,[status(thm)],[f117,f161]) ).
fof(f256,plain,
! [X0,X1] :
( unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(sK0_skl)),X1),X0)
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f244,f81]) ).
fof(f349,plain,
! [X0] :
( unequally_directed_lines(X0,sK0_skl)
| ~ unequally_directed_lines(X0,reverse_line(sK0_skl)) ),
inference(resolution,[status(thm)],[f149,f208]) ).
fof(f369,plain,
! [X0] : ~ unequally_directed_lines(X0,reverse_line(sK0_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f349,f149]) ).
fof(f372,plain,
unequally_directed_lines(sK0_skl,reverse_line(sK0_skl)),
inference(resolution,[status(thm)],[f369,f256]) ).
fof(f389,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f372,f369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO233+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 14:17:06 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.069346 seconds
% 0.14/0.44 % CPU time: 0.361303 seconds
% 0.14/0.44 % Total memory used: 15.879 MB
% 0.14/0.44 % Net memory used: 14.946 MB
%------------------------------------------------------------------------------