%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO223+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 : n012.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 12:24:36 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 64 ( 20 unt; 5 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 50 ~; 78 |; 12 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 103 ( 101 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f25,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f33,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f53,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f58,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f59,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f60,definition,
! [L,N] :
( sP0_prd(N,L)
<=> ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f61,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| sP0_prd(N,L)
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(formula_renaming,[status(thm)],[f59,f60]) ).
fof(f62,plain,
! [L,M] :
( ! [N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| sP0_prd(N,L) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f64,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X1,X2)
| sP0_prd(X2,X0)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
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] : distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f71,plain,
distinct_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(L,sK1_skl)],[f70]) ).
fof(f72,plain,
distinct_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [L,N] :
( ( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N)
| sP0_prd(N,L) )
& ( ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ sP0_prd(N,L) ) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f74,plain,
( ! [L,N] :
( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N)
| sP0_prd(N,L) )
& ! [L,N] :
( ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ sP0_prd(N,L) ) ),
inference(miniscoping,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f80,definition,
! [X0] :
( sQ0_spl
<=> ( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))
| apart_point_and_line(X0,parallel_through_point(sK1_skl,sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))
| apart_point_and_line(X0,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f90,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f81,f66]) ).
fof(f92,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f54]) ).
fof(f93,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f92]) ).
fof(f135,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[f58,f65]) ).
fof(f148,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f34,f135]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( convergent_lines(X1,X3)
| convergent_lines(orthogonal_through_point(X0,X2),X3)
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f148,f34]) ).
fof(f197,plain,
! [X0,X1,X2] :
( convergent_lines(X1,orthogonal_through_point(X0,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f150,f25]) ).
fof(f315,plain,
! [X0,X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)
| unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),X1)
| apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))
| apart_point_and_line(X0,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f69,f72]) ).
fof(f325,definition,
! [X1] :
( sQ7_spl
<=> ( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)
| unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f326,plain,
! [X0] :
( ~ sQ7_spl
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)
| unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),X0) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f315,f80,f325]) ).
fof(f338,plain,
( ~ sQ7_spl
| unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f326,f65]) ).
fof(f342,plain,
! [X0] :
( ~ sQ7_spl
| unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)
| sP0_prd(X0,parallel_through_point(sK1_skl,sK0_skl))
| ~ convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f338,f64]) ).
fof(f345,definition,
( sQ8_spl
<=> convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( sQ8_spl
| ~ convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f348,definition,
! [X0] :
( sQ9_spl
<=> ( unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)
| sP0_prd(X0,parallel_through_point(sK1_skl,sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f349,plain,
! [X0] :
( ~ sQ9_spl
| unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)
| sP0_prd(X0,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,plain,
( ~ sQ7_spl
| sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f342,f345,f348,f325]) ).
fof(f360,plain,
( sQ8_spl
| convergent_lines(sK1_skl,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f347,f197]) ).
fof(f361,plain,
! [X0] :
( sQ8_spl
| convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f360,f34]) ).
fof(f388,plain,
( sQ8_spl
| convergent_lines(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f361,f53]) ).
fof(f392,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f25]) ).
fof(f393,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f410,plain,
( ~ sQ9_spl
| sP0_prd(sK1_skl,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f349,f65]) ).
fof(f415,plain,
( ~ sQ9_spl
| convergent_lines(parallel_through_point(sK1_skl,sK0_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f410,f75]) ).
fof(f416,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f53]) ).
fof(f417,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f418,plain,
$false,
inference(sat_refutation,[status(thm)],[f93,f328,f351,f393,f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 20 13:47:07 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.32 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.40 % Elapsed time: 0.071508 seconds
% 0.07/0.40 % CPU time: 0.416912 seconds
% 0.07/0.40 % Total memory used: 24.995 MB
% 0.07/0.40 % Net memory used: 23.236 MB
%------------------------------------------------------------------------------