%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO189+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 : n009.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 12:24:23 PM UTC 2026
% Result : Theorem 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 10 unt; 5 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 168 ( 57 ~; 82 |; 18 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ apart_point_and_line(Y,line_connecting(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ apart_point_and_line(Y,line_connecting(X,Z)) ),
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(f35,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
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,Z] :
( apart_point_and_line(Y,line_connecting(X,Z))
& ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))
& ~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& distinct_points(sK1_skl,sK2_skl)
& distinct_points(sK0_skl,sK2_skl)
& distinct_points(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)],[f45]) ).
fof(f47,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
distinct_points(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f54,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f29,f15]) ).
fof(f56,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f30,f15]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4] :
( apart_point_and_line(X4,X3)
| ~ apart_point_and_line(X4,X2)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f36,f42]) ).
fof(f66,plain,
! [X0,X1,X2] :
( apart_point_and_line(sK1_skl,X2)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f65,f51]) ).
fof(f79,plain,
! [X0,X1] :
( ~ distinct_points(sK0_skl,sK2_skl)
| apart_point_and_line(sK1_skl,X1)
| apart_point_and_line(sK2_skl,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f66,f56]) ).
fof(f83,definition,
! [X0,X1] :
( sQ0_spl
<=> ( apart_point_and_line(sK1_skl,X1)
| apart_point_and_line(sK2_skl,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(X0,sK2_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f84,plain,
! [X0,X1] :
( ~ sQ0_spl
| apart_point_and_line(sK1_skl,X1)
| apart_point_and_line(sK2_skl,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(X0,sK2_skl) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,definition,
( sQ1_spl
<=> distinct_points(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( sQ1_spl
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f83,f86]) ).
fof(f94,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f48]) ).
fof(f95,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f103,plain,
! [X0] :
( ~ sQ0_spl
| ~ distinct_points(sK0_skl,sK2_skl)
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK0_skl,X0)
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f84,f54]) ).
fof(f113,definition,
! [X0] :
( sQ5_spl
<=> ( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
! [X0] :
( ~ sQ5_spl
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f103,f86,f113,f83]) ).
fof(f123,plain,
! [X0] :
( ~ sQ5_spl
| ~ distinct_points(X0,sK1_skl)
| apart_point_and_line(sK2_skl,line_connecting(X0,sK1_skl))
| apart_point_and_line(sK0_skl,line_connecting(X0,sK1_skl)) ),
inference(resolution,[status(thm)],[f114,f56]) ).
fof(f127,definition,
( sQ6_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ6_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f165,plain,
( ~ sQ6_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f128,f54]) ).
fof(f168,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f47]) ).
fof(f169,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f265,plain,
( ~ sQ5_spl
| ~ distinct_points(sK0_skl,sK1_skl)
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f123,f50]) ).
fof(f275,definition,
( sQ24_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( sQ24_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( ~ sQ5_spl
| ~ sQ24_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f265,f127,f275,f113]) ).
fof(f307,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f47]) ).
fof(f308,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f309,plain,
$false,
inference(sat_refutation,[status(thm)],[f89,f95,f116,f169,f278,f308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO189+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n009.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 20 13:09:48 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.15/5.42 % Refutation found
% 0.15/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.45 % Elapsed time: 0.060479 seconds
% 0.15/5.45 % CPU time: 0.290884 seconds
% 0.15/5.45 % Total memory used: 19.951 MB
% 0.15/5.45 % Net memory used: 19.174 MB
%------------------------------------------------------------------------------