%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:24:29 PM UTC 2026
% Result : Theorem 0.12s 0.57s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 10 unt; 2 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 75 ( 32 ~; 31 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 42 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(f13,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f27,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f48,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f49,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f50,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y)
| ~ distinct_lines(Y,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f51,plain,
! [Y,Z] :
( convergent_lines(Y,Z)
| ! [X] :
( apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) )
| ~ distinct_lines(Y,Z) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
? [X,Y,Z] :
( distinct_lines(Y,parallel_through_point(Z,X))
& ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
( distinct_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl))
& ~ convergent_lines(sK1_skl,sK2_skl)
& ~ apart_point_and_line(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f53]) ).
fof(f55,plain,
~ apart_point_and_line(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
~ convergent_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
distinct_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f63,plain,
! [X0] :
( convergent_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,parallel_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f52,f57]) ).
fof(f69,definition,
! [X0] :
( sQ0_spl
<=> ( apart_point_and_line(X0,parallel_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f70,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,parallel_through_point(sK2_skl,sK0_skl))
| apart_point_and_line(X0,sK1_skl) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,definition,
( sQ1_spl
<=> convergent_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( ~ sQ1_spl
| convergent_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f69,f72]) ).
fof(f76,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,parallel_through_point(sK2_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f70,f55]) ).
fof(f78,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f49]) ).
fof(f79,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0] :
( ~ sQ1_spl
| convergent_lines(parallel_through_point(sK2_skl,sK0_skl),X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f73,f29]) ).
fof(f84,plain,
( ~ sQ1_spl
| convergent_lines(parallel_through_point(sK2_skl,sK0_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f80,f56]) ).
fof(f90,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f48]) ).
fof(f91,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f90]) ).
fof(f92,plain,
$false,
inference(sat_refutation,[status(thm)],[f75,f79,f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.54 % Computer : n020.cluster.edu
% 0.08/0.54 % Model : x86_64 x86_64
% 0.08/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.54 % Memory : 8046.5625MB
% 0.08/0.54 % OS : Linux 6.8.0-71-generic
% 0.08/0.54 % CPULimit : 300
% 0.08/0.54 % WCLimit : 300
% 0.08/0.54 % DateTime : Sun Sep 20 13:29:02 UTC 2026
% 0.08/0.54 % CPUTime :
% 0.08/0.55 % Drodi V4.1.1
% 0.12/0.57 % Refutation found
% 0.12/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.59 % Elapsed time: 0.048152 seconds
% 0.12/0.59 % CPU time: 0.130015 seconds
% 0.12/0.59 % Total memory used: 17.218 MB
% 0.12/0.59 % Net memory used: 16.835 MB
%------------------------------------------------------------------------------