%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO210+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 : n003.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 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 86 ( 32 ~; 36 |; 12 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 64 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A,L,M] :
( ( orthogonal_lines(L,M)
& incident_point_and_line(A,L) )
=> equal_lines(L,orthogonal_through_point(M,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A,L,M] :
( ( orthogonal_lines(L,M)
& incident_point_and_line(A,L) )
=> equal_lines(L,orthogonal_through_point(M,A)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f83,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f84,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f85,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)],[f23]) ).
fof(f86,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)],[f85]) ).
fof(f87,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)],[f86]) ).
fof(f111,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f112,plain,
( ! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ! [X,Y] :
( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f119,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f120,plain,
( ! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ! [X,Y] :
( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f123,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f124,plain,
( ! [X,Y] :
( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ! [X,Y] :
( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
? [A,L,M] :
( ~ equal_lines(L,orthogonal_through_point(M,A))
& orthogonal_lines(L,M)
& incident_point_and_line(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ~ equal_lines(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl))
& orthogonal_lines(sK1_skl,sK2_skl)
& incident_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)],[f127]) ).
fof(f129,plain,
incident_point_and_line(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
orthogonal_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
~ equal_lines(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f144,plain,
distinct_lines(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl)),
inference(resolution,[status(thm)],[f131,f114]) ).
fof(f145,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)],[f144,f87]) ).
fof(f234,plain,
~ apart_point_and_line(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f121,f129]) ).
fof(f236,plain,
~ unorthogonal_lines(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f125,f130]) ).
fof(f246,plain,
! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),sK2_skl)
| apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f236,f145]) ).
fof(f248,plain,
! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f246,f83]) ).
fof(f278,plain,
apart_point_and_line(sK0_skl,orthogonal_through_point(sK2_skl,sK0_skl)),
inference(resolution,[status(thm)],[f248,f234]) ).
fof(f281,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f278,f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.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 13:26:44 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.066377 seconds
% 0.12/0.43 % CPU time: 0.345569 seconds
% 0.12/0.43 % Total memory used: 18.100 MB
% 0.12/0.43 % Net memory used: 17.427 MB
%------------------------------------------------------------------------------