%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO170+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 : n012.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 12:24:15 PM UTC 2026
% Result : Theorem 0.04s 0.42s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 11 unt; 7 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 136 ( 54 ~; 56 |; 14 &)
% ( 7 <=>; 5 =>; 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 : 43 ( 40 !; 3 ?)
% 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(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/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Y,Z)
& ~ apart_point_and_line(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_lines(Z,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(Y,Z)
& ~ apart_point_and_line(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_lines(Z,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(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(f45,plain,
? [X,Y,Z] :
( distinct_lines(Z,line_connecting(X,Y))
& ~ apart_point_and_line(Y,Z)
& ~ apart_point_and_line(X,Z)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,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)
& 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,
~ apart_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
~ apart_point_and_line(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f61,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X1,sK2_skl)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f36,f50]) ).
fof(f67,plain,
! [X0] :
( apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f61,f49]) ).
fof(f71,definition,
! [X0] :
( sQ0_spl
<=> ( apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f72,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,sK1_skl) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,definition,
( sQ1_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f71,f74]) ).
fof(f81,definition,
( sQ3_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f92,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f72,f47]) ).
fof(f98,definition,
( sQ4_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( ~ sQ4_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f101,plain,
( ~ sQ0_spl
| sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f92,f98,f81,f71]) ).
fof(f103,plain,
( ~ sQ3_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f82,f29]) ).
fof(f106,definition,
( sQ5_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( sQ5_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f110,definition,
( sQ6_spl
<=> distinct_points(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ6_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( ~ sQ3_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f103,f106,f110,f81]) ).
fof(f114,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f15]) ).
fof(f115,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f47]) ).
fof(f117,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f118,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f48]) ).
fof(f119,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f118]) ).
fof(f120,plain,
( ~ sQ1_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f75,f30]) ).
fof(f124,definition,
( sQ7_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ7_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( ~ sQ1_spl
| sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f120,f106,f124,f74]) ).
fof(f132,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f15]) ).
fof(f133,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f134,plain,
$false,
inference(sat_refutation,[status(thm)],[f77,f101,f113,f115,f117,f119,f127,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO170+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.39 % Computer : n012.cluster.edu
% 0.04/0.39 % Model : x86_64 x86_64
% 0.04/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.39 % Memory : 8046.5625MB
% 0.04/0.39 % OS : Linux 6.8.0-71-generic
% 0.04/0.39 % CPULimit : 300
% 0.04/0.39 % WCLimit : 300
% 0.04/0.39 % DateTime : Sun Sep 20 12:54:38 UTC 2026
% 0.04/0.40 % CPUTime :
% 0.04/0.40 % Drodi V4.1.1
% 0.04/0.42 % Refutation found
% 0.04/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.04/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.036767 seconds
% 0.09/0.44 % CPU time: 0.079331 seconds
% 0.09/0.44 % Total memory used: 17.374 MB
% 0.09/0.44 % Net memory used: 16.998 MB
%------------------------------------------------------------------------------