%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO190+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 : n016.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 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 10 unt; 10 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 190 ( 62 ~; 93 |; 18 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 75 !; 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,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(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,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(Z,line_connecting(Y,X)) ),
file('/export/starexec/sandbox/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(Z,line_connecting(Y,X)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
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(Z,line_connecting(Y,X))
& ~ 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(sK2_skl,line_connecting(sK1_skl,sK0_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(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(sK2_skl,line_connecting(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f54,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f20,f47]) ).
fof(f59,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK1_skl,X1)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f54,f20]) ).
fof(f62,definition,
( sQ0_spl
<=> distinct_points(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( sQ0_spl
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f74,plain,
( sQ0_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f64,f54]) ).
fof(f75,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f15]) ).
fof(f76,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f127,plain,
! [X0,X1] :
( distinct_points(X1,X0)
| distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f59,f20]) ).
fof(f134,definition,
( sQ8_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f137,definition,
! [X0,X1] :
( sQ9_spl
<=> ( distinct_points(X1,X0)
| distinct_points(sK1_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f138,plain,
! [X0,X1] :
( ~ sQ9_spl
| distinct_points(X1,X0)
| distinct_points(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f127,f134,f137]) ).
fof(f192,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f42,f51]) ).
fof(f207,plain,
( ~ sQ9_spl
| $false ),
inference(resolution,[status(thm)],[f138,f15]) ).
fof(f211,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f230,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(X1,X0)
| apart_point_and_line(X1,line_connecting(sK1_skl,sK0_skl))
| ~ distinct_points(X1,X2)
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f192,f36]) ).
fof(f446,plain,
! [X0] :
( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f230,f47]) ).
fof(f492,definition,
( sQ20_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( ~ sQ20_spl
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f499,definition,
( sQ22_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ22_spl
| apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f545,definition,
! [X0] :
( sQ33_spl
<=> ( apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK2_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f546,plain,
! [X0] :
( ~ sQ33_spl
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f585,plain,
( sQ20_spl
| sQ22_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f446,f545,f499,f492]) ).
fof(f659,plain,
( ~ sQ20_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f493,f29]) ).
fof(f663,definition,
( sQ54_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f664,plain,
( ~ sQ54_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f663]) ).
fof(f666,plain,
( ~ sQ20_spl
| sQ54_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f659,f62,f663,f492]) ).
fof(f667,plain,
( ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f664,f15]) ).
fof(f668,plain,
~ sQ54_spl,
inference(contradiction_clause,[status(thm)],[f667]) ).
fof(f670,plain,
( ~ sQ22_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f500,f30]) ).
fof(f674,definition,
( sQ55_spl
<=> distinct_points(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f675,plain,
( ~ sQ55_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f674]) ).
fof(f677,plain,
( ~ sQ22_spl
| sQ55_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f670,f62,f674,f499]) ).
fof(f679,plain,
( ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f675,f15]) ).
fof(f680,plain,
~ sQ55_spl,
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f935,plain,
( ~ sQ33_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f546,f50]) ).
fof(f940,definition,
( sQ71_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f941,plain,
( ~ sQ71_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f940]) ).
fof(f943,definition,
( sQ72_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f944,plain,
( ~ sQ72_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f943]) ).
fof(f946,plain,
( ~ sQ33_spl
| sQ72_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f935,f940,f943,f545]) ).
fof(f947,plain,
( ~ sQ71_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f941,f30]) ).
fof(f951,plain,
( ~ sQ71_spl
| sQ54_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f947,f134,f663,f940]) ).
fof(f954,plain,
( ~ sQ72_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f944,f29]) ).
fof(f958,plain,
( ~ sQ72_spl
| sQ55_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f954,f134,f674,f943]) ).
fof(f959,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f140,f211,f585,f666,f668,f677,f680,f946,f951,f958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO190+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 13:38:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.42 % Refutation found
% 0.10/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.072490 seconds
% 0.10/0.45 % CPU time: 0.305743 seconds
% 0.10/0.45 % Total memory used: 19.938 MB
% 0.10/0.45 % Net memory used: 19.213 MB
%------------------------------------------------------------------------------