%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO228+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 12:24:38 PM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 1 unt; 3 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 44 ~; 40 |; 9 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 22 ( 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f39,plain,
! [L,M] :
( ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
( ! [L,M] :
( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f130,plain,
? [L,M] :
( ~ convergent_lines(L,M)
<~> ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
? [L,M] :
( ( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
| convergent_lines(L,M) )
& ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| ~ convergent_lines(L,M) ) ),
inference(NNF_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
( ( ( unequally_directed_lines(sK0_skl,reverse_line(sK1_skl))
& unequally_directed_lines(sK0_skl,sK1_skl) )
| convergent_lines(sK0_skl,sK1_skl) )
& ( ~ unequally_directed_lines(sK0_skl,reverse_line(sK1_skl))
| ~ unequally_directed_lines(sK0_skl,sK1_skl)
| ~ convergent_lines(sK0_skl,sK1_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl)],[f131]) ).
fof(f133,plain,
( ~ unequally_directed_lines(sK0_skl,reverse_line(sK1_skl))
| ~ unequally_directed_lines(sK0_skl,sK1_skl)
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
( unequally_directed_lines(sK0_skl,sK1_skl)
| convergent_lines(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
( unequally_directed_lines(sK0_skl,reverse_line(sK1_skl))
| convergent_lines(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f141,definition,
( sQ0_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ0_spl
| convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ1_spl
<=> unequally_directed_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ1_spl
| ~ unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ2_spl
<=> unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ2_spl
| unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f133,f141,f144,f147]) ).
fof(f151,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f134,f141,f144]) ).
fof(f152,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f135,f141,f147]) ).
fof(f153,plain,
( ~ sQ0_spl
| unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f41,f142]) ).
fof(f154,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f146]) ).
fof(f155,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f158,plain,
( ~ sQ2_spl
| ~ unequally_directed_lines(sK0_skl,sK1_skl)
| convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f43,f148]) ).
fof(f159,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f158,f141,f144,f147]) ).
fof(f160,plain,
( ~ sQ0_spl
| unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)) ),
inference(resolution,[status(thm)],[f142,f42]) ).
fof(f162,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f160,f147,f141]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f150,f151,f152,f155,f159,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO228+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n016.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 14:11:52 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.045309 seconds
% 0.08/0.42 % CPU time: 0.118544 seconds
% 0.08/0.42 % Total memory used: 18.963 MB
% 0.08/0.42 % Net memory used: 18.898 MB
%------------------------------------------------------------------------------