%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO179+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:24:19 PM UTC 2026
% Result : Theorem 0.13s 0.58s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 6 unt; 6 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 47 ~; 64 |; 8 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 72 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
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(f36,conjecture,
! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f41,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f50,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f51,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f60,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(f61,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,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)],[f61]) ).
fof(f63,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(f64,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,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)],[f64]) ).
fof(f127,plain,
? [X,Y,Z] :
( ( ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
| ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) )
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ( ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl))
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) )
& apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_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)],[f127]) ).
fof(f129,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
( ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl))
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f142,definition,
( sQ0_spl
<=> distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( sQ0_spl
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
( sQ1_spl
<=> distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ1_spl
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f131,f142,f145]) ).
fof(f149,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f43,f129]) ).
fof(f150,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK1_skl,X1)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f149,f43]) ).
fof(f158,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(sK0_skl,X2)
| distinct_points(X1,X0)
| distinct_points(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f150,f43]) ).
fof(f174,definition,
( sQ4_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK0_skl,X1)
| distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f158,f38]) ).
fof(f199,definition,
! [X1,X2] :
( sQ7_spl
<=> ( distinct_points(X2,X1)
| distinct_points(sK0_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0,X1] :
( ~ sQ7_spl
| distinct_points(X1,X0)
| distinct_points(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f207,plain,
! [X0] :
( apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| distinct_points(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f62,f130]) ).
fof(f208,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f65,f130]) ).
fof(f228,plain,
! [X0,X1] :
( distinct_points(X1,X0)
| distinct_points(sK0_skl,X0)
| distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f185,f43]) ).
fof(f234,plain,
( sQ7_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f228,f174,f199]) ).
fof(f237,plain,
( ~ sQ7_spl
| $false ),
inference(resolution,[status(thm)],[f200,f38]) ).
fof(f241,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f246,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f207,f53]) ).
fof(f247,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| distinct_points(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f207,f51]) ).
fof(f250,definition,
( sQ8_spl
<=> distinct_points(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( ~ sQ8_spl
| distinct_points(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( ~ sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f246,f250,f174]) ).
fof(f254,definition,
( sQ9_spl
<=> distinct_points(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ9_spl
| distinct_points(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( ~ sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f247,f254,f174]) ).
fof(f268,plain,
( sQ0_spl
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f208,f144]) ).
fof(f276,plain,
( sQ0_spl
| ~ distinct_points(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f268,f51]) ).
fof(f279,plain,
( sQ0_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f276,f255]) ).
fof(f280,plain,
( sQ0_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f279]) ).
fof(f311,plain,
( sQ1_spl
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f147,f208]) ).
fof(f312,plain,
( sQ1_spl
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f311,f51]) ).
fof(f315,plain,
( sQ1_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f251]) ).
fof(f316,plain,
( sQ1_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f317,plain,
$false,
inference(sat_refutation,[status(thm)],[f148,f234,f241,f253,f257,f280,f316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO179+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.54 % Computer : n019.cluster.edu
% 0.10/0.54 % Model : x86_64 x86_64
% 0.10/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.54 % Memory : 8046.5625MB
% 0.10/0.54 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Sun Sep 20 13:33:24 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.55 % Drodi V4.1.1
% 0.13/0.58 % Refutation found
% 0.13/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.60 % Elapsed time: 0.048429 seconds
% 0.13/0.60 % CPU time: 0.150288 seconds
% 0.13/0.60 % Total memory used: 18.649 MB
% 0.13/0.60 % Net memory used: 18.527 MB
%------------------------------------------------------------------------------