%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO222+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 : n004.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 0.19s 0.74s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 18 unt; 6 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 182 ( 67 ~; 89 |; 14 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 113 ( 111 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f8,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
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(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] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f39,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f40,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) ) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f51,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
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(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] : convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f71,plain,
convergent_lines(sK1_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,
convergent_lines(sK1_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(f100,plain,
distinct_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)),
inference(resolution,[status(thm)],[f52,f72]) ).
fof(f103,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[f58,f65]) ).
fof(f105,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f103,f34]) ).
fof(f115,plain,
! [X0,X1] : convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(resolution,[status(thm)],[f105,f25]) ).
fof(f129,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f41,f23]) ).
fof(f131,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f42,f23]) ).
fof(f150,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,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f151,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,sK1_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ1_spl
<=> convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ1_spl
| ~ convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f162,plain,
! [X0] :
( ~ sQ0_spl
| ~ convergent_lines(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))
| apart_point_and_line(intersection_point(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)),sK1_skl) ),
inference(resolution,[status(thm)],[f151,f131]) ).
fof(f388,plain,
( ~ sQ0_spl
| ~ convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))
| ~ convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)) ),
inference(resolution,[status(thm)],[f162,f129]) ).
fof(f391,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f388,f153,f150]) ).
fof(f392,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f72]) ).
fof(f393,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f394,plain,
! [X0,X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)
| unorthogonal_lines(sK1_skl,X1)
| apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f100,f69]) ).
fof(f398,definition,
! [X1] :
( sQ2_spl
<=> ( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)
| unorthogonal_lines(sK1_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f399,plain,
! [X0] :
( ~ sQ2_spl
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)
| unorthogonal_lines(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f394,f150,f398]) ).
fof(f458,plain,
( ~ sQ2_spl
| unorthogonal_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f399,f65]) ).
fof(f466,plain,
! [X0] :
( ~ sQ2_spl
| unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)
| sP0_prd(X0,sK1_skl)
| ~ convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f458,f64]) ).
fof(f469,definition,
( sQ5_spl
<=> convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ5_spl
| ~ convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,definition,
! [X0] :
( sQ6_spl
<=> ( unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)
| sP0_prd(X0,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f473,plain,
! [X0] :
( ~ sQ6_spl
| unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)
| sP0_prd(X0,sK1_skl) ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,plain,
( ~ sQ2_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f466,f469,f472,f398]) ).
fof(f484,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f115]) ).
fof(f485,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f488,plain,
( ~ sQ6_spl
| sP0_prd(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f473,f65]) ).
fof(f493,plain,
( ~ sQ6_spl
| convergent_lines(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f488,f75]) ).
fof(f494,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f25]) ).
fof(f495,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f496,plain,
$false,
inference(sat_refutation,[status(thm)],[f391,f393,f401,f475,f485,f495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 % Computer : n004.cluster.edu
% 0.19/0.42 % Model : x86_64 x86_64
% 0.19/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42 % Memory : 8046.5625MB
% 0.19/0.42 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Sun Sep 20 13:49:50 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.44 % Drodi V4.1.1
% 0.19/0.74 % Refutation found
% 0.19/0.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.26/0.80 % Elapsed time: 0.348579 seconds
% 1.26/0.80 % CPU time: 2.120237 seconds
% 1.26/0.80 % Total memory used: 33.810 MB
% 1.26/0.80 % Net memory used: 29.724 MB
%------------------------------------------------------------------------------