%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO210+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 : n018.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 12:24:31 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 10 unt; 2 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 28 ~; 29 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [A,L,M] :
( ( ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [A,L,M] :
( ( ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f65,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f66,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f67,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f68,plain,
! [L,M] :
( ! [N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| ! [A] :
( apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) )
| ~ distinct_lines(L,M) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
? [A,L,M] :
( distinct_lines(L,orthogonal_through_point(M,A))
& ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f71,plain,
( distinct_lines(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl))
& ~ unorthogonal_lines(sK1_skl,sK2_skl)
& ~ apart_point_and_line(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(L,sK1_skl),skolemize(M,sK2_skl)],[f70]) ).
fof(f72,plain,
~ apart_point_and_line(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
~ unorthogonal_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f74,plain,
distinct_lines(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f130,definition,
! [X0] :
( sQ3_spl
<=> ( apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f131,plain,
! [X0] :
( ~ sQ3_spl
| apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,sK1_skl) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f144,plain,
! [X0,X1] :
( unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X1)
| unorthogonal_lines(sK1_skl,X1)
| apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f69,f74]) ).
fof(f151,definition,
! [X1] :
( sQ6_spl
<=> ( unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X1)
| unorthogonal_lines(sK1_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ6_spl
| unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X0)
| unorthogonal_lines(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( sQ6_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f144,f130,f151]) ).
fof(f271,plain,
( ~ sQ3_spl
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f131,f66]) ).
fof(f276,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f72]) ).
fof(f277,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f296,plain,
( ~ sQ6_spl
| unorthogonal_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f152,f65]) ).
fof(f298,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f73]) ).
fof(f299,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f300,plain,
$false,
inference(sat_refutation,[status(thm)],[f154,f277,f299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO210+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.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 13:27:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.051260 seconds
% 0.13/0.43 % CPU time: 0.183473 seconds
% 0.13/0.43 % Total memory used: 18.404 MB
% 0.13/0.43 % Net memory used: 18.065 MB
%------------------------------------------------------------------------------