%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:24:47 PM UTC 2026
% Result : Theorem 0.08s 0.41s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 11 unt; 2 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 60 ~; 53 |; 14 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 79 ( 78 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [L] : equally_directed_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L] : equally_directed_opposite_lines(L,reverse_line(L)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L] : equally_directed_opposite_lines(L,reverse_line(L)),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f40,plain,
( ! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ! [X,Y] :
( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
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(f55,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f56,plain,
( ! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ! [X,Y] :
( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f58,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f64,plain,
! [L,M] :
( ( ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f65,plain,
( ! [L,M] :
( ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ! [L,M] :
( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
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_opposite_lines(L,reverse_line(L)),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
~ equally_directed_opposite_lines(sK0_skl,reverse_line(sK0_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(L,sK0_skl)],[f152]) ).
fof(f154,plain,
~ equally_directed_opposite_lines(sK0_skl,reverse_line(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(f179,plain,
! [X0,X1] :
( equally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f68,f58]) ).
fof(f185,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| equally_directed_opposite_lines(X0,reverse_line(X1))
| convergent_lines(X0,reverse_line(X1)) ),
inference(resolution,[status(thm)],[f179,f110]) ).
fof(f198,definition,
( sQ0_spl
<=> convergent_lines(sK0_skl,reverse_line(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ0_spl
| convergent_lines(sK0_skl,reverse_line(sK0_skl)) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f206,plain,
( unequally_directed_lines(sK0_skl,sK0_skl)
| convergent_lines(sK0_skl,reverse_line(sK0_skl)) ),
inference(resolution,[status(thm)],[f185,f154]) ).
fof(f208,definition,
( sQ2_spl
<=> unequally_directed_lines(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ2_spl
| unequally_directed_lines(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f206,f198,f208]) ).
fof(f212,plain,
( ~ sQ0_spl
| unequally_directed_opposite_lines(sK0_skl,reverse_line(sK0_skl)) ),
inference(resolution,[status(thm)],[f199,f67]) ).
fof(f213,plain,
( ~ sQ0_spl
| unequally_directed_lines(sK0_skl,reverse_line(sK0_skl)) ),
inference(resolution,[status(thm)],[f199,f66]) ).
fof(f246,plain,
( ~ sQ2_spl
| ~ equally_directed_lines(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f209,f53]) ).
fof(f248,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f246,f100]) ).
fof(f249,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f272,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f171,f41]) ).
fof(f278,plain,
( ~ sQ0_spl
| ~ unequally_directed_lines(sK0_skl,reverse_line(sK0_skl)) ),
inference(resolution,[status(thm)],[f272,f212]) ).
fof(f283,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f213]) ).
fof(f284,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f285,plain,
$false,
inference(sat_refutation,[status(thm)],[f211,f249,f284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.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 15:03:28 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.41 % Refutation found
% 0.08/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.43 % Elapsed time: 0.054805 seconds
% 0.08/0.43 % CPU time: 0.211261 seconds
% 0.08/0.43 % Total memory used: 20.263 MB
% 0.08/0.43 % Net memory used: 20.055 MB
%------------------------------------------------------------------------------