%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO174+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:24:16 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% 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 : 7 ( 6 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(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,U,V] :
( ( ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_lines(U,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_lines(U,line_connecting(X,Y)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f29,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f42,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f48,plain,
? [X,Y,U,V] :
( ~ distinct_lines(U,line_connecting(X,Y))
& ( apart_point_and_line(Y,U)
| 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,Y,U] :
( ~ distinct_lines(U,line_connecting(X,Y))
& ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& ? [V] : convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ~ distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& ( apart_point_and_line(sK1_skl,sK2_skl)
| apart_point_and_line(sK0_skl,sK2_skl) )
& convergent_lines(sK2_skl,sK3_skl)
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f49]) ).
fof(f51,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
( apart_point_and_line(sK1_skl,sK2_skl)
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
~ distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,definition,
( sQ0_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,definition,
( sQ1_spl
<=> apart_point_and_line(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ1_spl
| apart_point_and_line(sK1_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(f73,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f44,f56]) ).
fof(f74,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f73,f54]) ).
fof(f77,plain,
( ~ sQ0_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f74,f30]) ).
fof(f79,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f51]) ).
fof(f80,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f59,f44]) ).
fof(f82,plain,
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f81,f54]) ).
fof(f85,plain,
( ~ sQ1_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f82,f32]) ).
fof(f87,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f51]) ).
fof(f88,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f87]) ).
fof(f89,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f80,f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO174+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:00:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.033807 seconds
% 0.09/0.40 % CPU time: 0.090621 seconds
% 0.09/0.40 % Total memory used: 11.745 MB
% 0.09/0.40 % Net memory used: 11.459 MB
%------------------------------------------------------------------------------