%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO204+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 : n002.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 12:24:29 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 7 unt; 7 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 160 ( 64 ~; 73 |; 9 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 58 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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(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,Z] :
( ( ~ distinct_points(Y,Z)
& distinct_points(X,Y) )
=> ( ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ distinct_points(Y,Z)
& distinct_points(X,Y) )
=> ( ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f20,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
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(f37,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)],[f11]) ).
fof(f38,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)],[f37]) ).
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,Z] :
( ( distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
| ~ distinct_points(X,Z) )
& ~ distinct_points(Y,Z)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( ( distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(sK0_skl,sK2_skl) )
& ~ distinct_points(sK1_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)],[f48]) ).
fof(f50,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
~ distinct_points(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
( distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,definition,
( sQ0_spl
<=> distinct_points(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ0_spl
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ1_spl
| distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56]) ).
fof(f60,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f22,f50]) ).
fof(f61,plain,
distinct_points(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f60,f51]) ).
fof(f64,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f55]) ).
fof(f65,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f69,plain,
! [X0,X1] :
( ~ sQ1_spl
| apart_point_and_line(X1,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f57,f38]) ).
fof(f74,plain,
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f69,f50]) ).
fof(f78,definition,
( sQ3_spl
<=> apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ3_spl
| apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f80,plain,
( sQ3_spl
| ~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f85,definition,
( sQ5_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ5_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ6_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ6_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f92,definition,
( sQ7_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( ~ sQ7_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
( sQ8_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ8_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f99,plain,
( ~ sQ1_spl
| sQ6_spl
| sQ5_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f74,f92,f95,f85,f88,f56]) ).
fof(f104,plain,
! [X0] :
( ~ sQ6_spl
| apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))
| distinct_points(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f89,f41]) ).
fof(f105,plain,
( ~ sQ5_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f86,f32]) ).
fof(f108,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f50]) ).
fof(f109,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f110,plain,
( ~ sQ8_spl
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f96,f30]) ).
fof(f113,plain,
( ~ sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f110,f53,f95]) ).
fof(f170,plain,
( ~ sQ7_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f93,f30]) ).
fof(f173,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f50]) ).
fof(f174,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f291,plain,
( ~ sQ3_spl
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f79,f32]) ).
fof(f294,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f291,f53,f78]) ).
fof(f362,plain,
( sQ3_spl
| ~ sQ6_spl
| distinct_points(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f104,f80]) ).
fof(f370,plain,
( sQ3_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f362,f51]) ).
fof(f371,plain,
( sQ3_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f372,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f65,f99,f109,f113,f174,f294,f371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO204+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 13:27:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.048835 seconds
% 0.13/0.44 % CPU time: 0.131327 seconds
% 0.13/0.44 % Total memory used: 17.337 MB
% 0.13/0.44 % Net memory used: 16.939 MB
%------------------------------------------------------------------------------