%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO174+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 : n017.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 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 6 unt; 3 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 35 ~; 38 |; 16 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,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(f13,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(f14,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)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X,Y] :
( ! [Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y)) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f40,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)],[f11]) ).
fof(f41,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f45,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)],[f14]) ).
fof(f46,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)],[f45]) ).
fof(f47,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)],[f46]) ).
fof(f48,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
( apart_point_and_line(sK1_skl,sK2_skl)
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
~ distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,definition,
( sQ0_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,definition,
( sQ1_spl
<=> apart_point_and_line(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f52,f55]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( distinct_points(X0,X3)
| ~ distinct_points(X2,X3)
| distinct_lines(X1,line_connecting(X2,X3))
| ~ apart_point_and_line(X0,X1) ),
inference(resolution,[status(thm)],[f42,f30]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( distinct_points(X0,X2)
| ~ distinct_points(X2,X3)
| distinct_lines(X1,line_connecting(X2,X3))
| ~ apart_point_and_line(X0,X1) ),
inference(resolution,[status(thm)],[f42,f29]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ distinct_points(X2,X0)
| distinct_lines(X1,line_connecting(X2,X0))
| ~ apart_point_and_line(X0,X1) ),
inference(resolution,[status(thm)],[f83,f15]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X2)
| distinct_lines(X1,line_connecting(X0,X2))
| ~ apart_point_and_line(X0,X1) ),
inference(resolution,[status(thm)],[f84,f15]) ).
fof(f141,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| ~ apart_point_and_line(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f104,f51]) ).
fof(f145,definition,
( sQ2_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ2_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f141,f55,f145]) ).
fof(f149,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f48]) ).
fof(f150,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f173,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| ~ apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f105,f51]) ).
fof(f177,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f173,f52,f145]) ).
fof(f178,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f148,f150,f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n017.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 20 12:58:56 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.20/0.41 % Drodi V4.1.1
% 0.20/0.43 % Refutation found
% 0.20/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.50 % Elapsed time: 0.085121 seconds
% 0.20/0.50 % CPU time: 0.116204 seconds
% 0.20/0.50 % Total memory used: 4.661 MB
% 0.20/0.50 % Net memory used: 4.554 MB
%------------------------------------------------------------------------------