%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 0.13s 0.51s
% Output : CNFRefutation 0.13s
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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(f23,conjecture,
! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,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)],[f23]) ).
fof(f27,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f34,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f56,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f57,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f61,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f62,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)],[f19]) ).
fof(f63,definition,
! [L,N] :
( sP0_prd(N,L)
<=> ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f64,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)],[f62,f63]) ).
fof(f65,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)],[f64]) ).
fof(f67,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)],[f65]) ).
fof(f68,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f69,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f70,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)],[f22]) ).
fof(f71,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)],[f70]) ).
fof(f72,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)],[f71]) ).
fof(f73,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)],[f24]) ).
fof(f74,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)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f76,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)],[f63]) ).
fof(f77,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)],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f83,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(f84,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)],[f83]) ).
fof(f93,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f84,f69]) ).
fof(f95,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f57]) ).
fof(f96,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f95]) ).
fof(f128,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[f61,f68]) ).
fof(f140,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f36,f128]) ).
fof(f142,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)],[f140,f36]) ).
fof(f206,plain,
! [X0,X1,X2] :
( convergent_lines(X1,orthogonal_through_point(X0,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f142,f27]) ).
fof(f283,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)],[f72,f75]) ).
fof(f292,definition,
! [X1] :
( sQ5_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,[sQ5_spl])],[split_symbol_definition]) ).
fof(f293,plain,
! [X0] :
( ~ sQ5_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)],[f292]) ).
fof(f295,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f283,f83,f292]) ).
fof(f296,plain,
( ~ sQ5_spl
| unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f293,f68]) ).
fof(f304,plain,
! [X0] :
( ~ sQ5_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)],[f296,f67]) ).
fof(f307,definition,
( sQ6_spl
<=> convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ6_spl
| ~ convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,definition,
! [X0] :
( sQ7_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,[sQ7_spl])],[split_symbol_definition]) ).
fof(f311,plain,
! [X0] :
( ~ sQ7_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)],[f310]) ).
fof(f313,plain,
( ~ sQ5_spl
| sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f304,f307,f310,f292]) ).
fof(f322,plain,
( sQ6_spl
| convergent_lines(sK1_skl,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f309,f206]) ).
fof(f324,plain,
! [X0] :
( sQ6_spl
| convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f322,f36]) ).
fof(f341,plain,
( sQ6_spl
| convergent_lines(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f324,f56]) ).
fof(f345,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f27]) ).
fof(f346,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f399,plain,
( ~ sQ7_spl
| sP0_prd(sK1_skl,parallel_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f311,f68]) ).
fof(f404,plain,
( ~ sQ7_spl
| convergent_lines(parallel_through_point(sK1_skl,sK0_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f399,f78]) ).
fof(f405,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f56]) ).
fof(f406,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f407,plain,
$false,
inference(sat_refutation,[status(thm)],[f96,f295,f313,f346,f406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 13:53:05 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.13/0.51 % Refutation found
% 0.13/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.53 % Elapsed time: 0.156635 seconds
% 0.13/0.53 % CPU time: 0.991805 seconds
% 0.13/0.53 % Total memory used: 28.736 MB
% 0.13/0.53 % Net memory used: 26.339 MB
%------------------------------------------------------------------------------