%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO208+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 : n003.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 12:24:30 PM UTC 2026
% Result : Theorem 0.08s 5.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 7 unt; 2 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 70 ( 31 ~; 21 |; 13 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 27 ( 21 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,Z) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
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,Z)
& ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Z)
& ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
? [Y,Z] :
( distinct_lines(Y,Z)
& ~ convergent_lines(Y,Z)
& ? [X] :
( ~ apart_point_and_line(X,Z)
& ~ apart_point_and_line(X,Y) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
( distinct_lines(sK0_skl,sK1_skl)
& ~ convergent_lines(sK0_skl,sK1_skl)
& ~ apart_point_and_line(sK2_skl,sK1_skl)
& ~ apart_point_and_line(sK2_skl,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Y,sK0_skl),skolemize(Z,sK1_skl),skolemize(X,sK2_skl)],[f54]) ).
fof(f56,plain,
~ apart_point_and_line(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
~ apart_point_and_line(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
~ convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,plain,
distinct_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f65,plain,
! [X0] :
( convergent_lines(sK0_skl,sK1_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f52,f59]) ).
fof(f71,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(f72,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,definition,
( sQ1_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ1_spl
| convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f71,f74]) ).
fof(f78,plain,
( ~ sQ0_spl
| apart_point_and_line(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f72,f57]) ).
fof(f80,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f56]) ).
fof(f81,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f80]) ).
fof(f82,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f58]) ).
fof(f83,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f82]) ).
fof(f84,plain,
$false,
inference(sat_refutation,[status(thm)],[f77,f81,f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO208+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n003.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sun Sep 20 13:29:05 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.08/5.39 % Refutation found
% 0.08/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.036756 seconds
% 0.13/5.42 % CPU time: 0.114999 seconds
% 0.13/5.42 % Total memory used: 17.143 MB
% 0.13/5.42 % Net memory used: 16.762 MB
%------------------------------------------------------------------------------