%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO176+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 : n014.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 12:24:17 PM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 5 unt; 2 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 82 ( 32 ~; 30 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 34 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,U,V] :
( ( ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_points(X,intersection_point(U,V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_points(X,intersection_point(U,V)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f33,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f48,plain,
? [X,Y,U,V] :
( ~ distinct_points(X,intersection_point(U,V))
& ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
? [X,U,V] :
( ~ distinct_points(X,intersection_point(U,V))
& ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& ? [Y] : distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ~ distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))
& ( apart_point_and_line(sK0_skl,sK2_skl)
| apart_point_and_line(sK0_skl,sK1_skl) )
& convergent_lines(sK1_skl,sK2_skl)
& distinct_points(sK0_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(Y,sK3_skl)],[f49]) ).
fof(f52,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
( apart_point_and_line(sK0_skl,sK2_skl)
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
~ distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,definition,
( sQ0_spl
<=> apart_point_and_line(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,definition,
( sQ1_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ1_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f55,f58]) ).
fof(f70,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,sK1_skl)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f41,f56]) ).
fof(f71,plain,
( ~ sQ0_spl
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f70,f54]) ).
fof(f76,plain,
( ~ sQ0_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f71,f34]) ).
fof(f78,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f52]) ).
fof(f79,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0] :
( ~ sQ1_spl
| apart_point_and_line(X0,sK2_skl)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f59,f41]) ).
fof(f83,plain,
( ~ sQ1_spl
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f80,f54]) ).
fof(f86,plain,
( ~ sQ1_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f83,f36]) ).
fof(f88,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f52]) ).
fof(f89,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f90,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f79,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO176+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 12:57:34 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.08/0.36 % Refutation found
% 0.08/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.038012 seconds
% 0.12/0.39 % CPU time: 0.066872 seconds
% 0.12/0.39 % Total memory used: 4.097 MB
% 0.12/0.39 % Net memory used: 4.026 MB
%------------------------------------------------------------------------------