%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO227+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 : n013.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 12:24:37 PM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 8 unt; 3 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 26 ~; 17 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 12 ( 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [L,M] :
( ( line(M)
& line(L) )
=> ( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [L,M] :
( ( line(M)
& line(L) )
=> ~ ( ~ 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] :
( ( line(M)
& line(L) )
=> ~ ( ~ unequally_directed_lines(L,reverse_line(M))
& ~ unequally_directed_lines(L,M) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f88,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M)
| ~ line(M)
| ~ line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f89,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f130,plain,
? [L,M] :
( ~ unequally_directed_lines(L,reverse_line(M))
& ~ unequally_directed_lines(L,M)
& line(M)
& line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
( ~ unequally_directed_lines(sK0_skl,reverse_line(sK1_skl))
& ~ unequally_directed_lines(sK0_skl,sK1_skl)
& line(sK1_skl)
& line(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl)],[f130]) ).
fof(f132,plain,
line(sK0_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
line(sK1_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
~ unequally_directed_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f135,plain,
~ unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f156,plain,
( unequally_directed_lines(sK0_skl,sK1_skl)
| ~ line(sK1_skl)
| ~ line(sK0_skl) ),
inference(resolution,[status(thm)],[f135,f89]) ).
fof(f157,definition,
( sQ0_spl
<=> line(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( sQ0_spl
| ~ line(sK0_skl) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
( sQ1_spl
<=> line(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( sQ1_spl
| ~ line(sK1_skl) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
( sQ2_spl
<=> unequally_directed_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ2_spl
| unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f156,f157,f160,f163]) ).
fof(f167,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f134]) ).
fof(f168,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f132]) ).
fof(f170,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f171,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f133]) ).
fof(f172,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f173,plain,
$false,
inference(sat_refutation,[status(thm)],[f166,f168,f170,f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO227+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 % Computer : n013.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Sun Sep 20 14:00:21 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.49 % Drodi V4.1.1
% 0.17/0.51 % Refutation found
% 0.17/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.55 % Elapsed time: 0.076259 seconds
% 0.17/0.55 % CPU time: 0.078914 seconds
% 0.17/0.55 % Total memory used: 1.822 MB
% 0.17/0.55 % Net memory used: 1.805 MB
%------------------------------------------------------------------------------