%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO216+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:24:33 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 17 ~; 9 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 23 ( 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [L] :
~ ~ unorthogonal_lines(L,L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [L] :
~ ~ unorthogonal_lines(L,L),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f48,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f49,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f56,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f57,plain,
! [M,N] :
( ~ convergent_lines(M,N)
| ! [L] :
( unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
? [L] : ~ unorthogonal_lines(L,L),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f60,plain,
~ unorthogonal_lines(sK0_skl,sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(L,sK0_skl)],[f59]) ).
fof(f61,plain,
~ unorthogonal_lines(sK0_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f67,plain,
convergent_lines(sK0_skl,sK0_skl),
inference(resolution,[status(thm)],[f49,f61]) ).
fof(f68,plain,
! [X0] :
( unorthogonal_lines(X0,sK0_skl)
| unorthogonal_lines(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f58,f67]) ).
fof(f69,plain,
! [X0] : unorthogonal_lines(X0,sK0_skl),
inference(duplicate_literals_removal,[status(thm)],[f68]) ).
fof(f71,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f61,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO216+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:36:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.044801 seconds
% 0.09/0.42 % CPU time: 0.115619 seconds
% 0.09/0.42 % Total memory used: 17.203 MB
% 0.09/0.42 % Net memory used: 16.808 MB
%------------------------------------------------------------------------------