%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO215+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 : n015.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 12:24:33 PM UTC 2026
% Result : Theorem 0.10s 0.47s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 9 unt; 4 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 110 ( 42 ~; 52 |; 6 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
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,
! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f27,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f53,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
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,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ unorthogonal_lines(L,N)
& convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f74,plain,
? [L,M] :
( ? [N] :
( ~ unorthogonal_lines(M,N)
& ~ unorthogonal_lines(L,N) )
& convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f73]) ).
fof(f75,plain,
( ~ unorthogonal_lines(sK1_skl,sK2_skl)
& ~ unorthogonal_lines(sK0_skl,sK2_skl)
& convergent_lines(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl),skolemize(N,sK2_skl)],[f74]) ).
fof(f76,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
~ unorthogonal_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f78,plain,
~ unorthogonal_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f199,plain,
! [X0] :
( convergent_lines(sK0_skl,X0)
| distinct_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f55,f76]) ).
fof(f249,definition,
! [X0] :
( sQ0_spl
<=> ( apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f250,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,definition,
( sQ1_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ1_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f261,plain,
! [X0] :
( ~ sQ0_spl
| ~ convergent_lines(X0,sK1_skl)
| apart_point_and_line(intersection_point(X0,sK1_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f250,f44]) ).
fof(f456,plain,
! [X0,X1,X2] :
( convergent_lines(sK0_skl,X1)
| unorthogonal_lines(X1,X2)
| unorthogonal_lines(sK1_skl,X2)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f72,f199]) ).
fof(f517,plain,
! [X0] :
( convergent_lines(sK0_skl,sK0_skl)
| unorthogonal_lines(sK1_skl,sK2_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f456,f77]) ).
fof(f540,definition,
( sQ21_spl
<=> unorthogonal_lines(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( ~ sQ21_spl
| unorthogonal_lines(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f544,definition,
( sQ22_spl
<=> convergent_lines(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( ~ sQ22_spl
| convergent_lines(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,plain,
( sQ22_spl
| sQ21_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f517,f249,f540,f544]) ).
fof(f680,plain,
( ~ sQ0_spl
| ~ convergent_lines(sK0_skl,sK1_skl)
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f261,f42]) ).
fof(f683,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f680,f252,f249]) ).
fof(f685,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f76]) ).
fof(f686,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f685]) ).
fof(f687,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f78]) ).
fof(f688,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f687]) ).
fof(f689,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f27]) ).
fof(f690,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f689]) ).
fof(f691,plain,
$false,
inference(sat_refutation,[status(thm)],[f547,f683,f686,f688,f690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO215+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 13:33:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.47 % Refutation found
% 0.10/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.48 % Elapsed time: 0.105521 seconds
% 0.10/0.48 % CPU time: 0.615459 seconds
% 0.10/0.48 % Total memory used: 23.066 MB
% 0.10/0.48 % Net memory used: 21.705 MB
%------------------------------------------------------------------------------