%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO180+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 : n010.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 0.50s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 10 unt; 10 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 164 ( 58 ~; 78 |; 10 &)
% ( 10 <=>; 8 =>; 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 : 59 ( 53 !; 6 ?)
% 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(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] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(X,line_connecting(Z,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(X,line_connecting(Z,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(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(X,line_connecting(Z,Y))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
? [X,Y] :
( ? [Z] :
( ~ apart_point_and_line(X,line_connecting(Z,Y))
& apart_point_and_line(Z,line_connecting(X,Y)) )
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_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)],[f46]) ).
fof(f48,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
~ apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f53,definition,
( sQ0_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ0_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f60,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f48]) ).
fof(f61,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( distinct_points(sK2_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f30,f49]) ).
fof(f63,definition,
( sQ2_spl
<=> distinct_points(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f53,f63]) ).
fof(f77,plain,
! [X0,X1] :
( apart_point_and_line(sK1_skl,X1)
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X1)
| apart_point_and_line(sK0_skl,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f36,f48]) ).
fof(f80,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f42,f49]) ).
fof(f129,plain,
! [X0] :
( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f80,f77]) ).
fof(f132,definition,
! [X0] :
( sQ5_spl
<=> ( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK2_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f133,plain,
! [X0] :
( ~ sQ5_spl
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,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(f136,plain,
( ~ sQ6_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,definition,
( sQ7_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ7_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f129,f132,f135,f138]) ).
fof(f188,plain,
( ~ sQ7_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f139,f30]) ).
fof(f192,definition,
( sQ16_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ16_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( ~ sQ7_spl
| sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f188,f53,f192,f138]) ).
fof(f201,plain,
( ~ sQ6_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f136,f29]) ).
fof(f205,definition,
( sQ18_spl
<=> distinct_points(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ18_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ6_spl
| sQ18_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f201,f53,f205,f135]) ).
fof(f209,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f15]) ).
fof(f210,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f15]) ).
fof(f212,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f299,plain,
( ~ sQ5_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f133,f50]) ).
fof(f310,definition,
( sQ25_spl
<=> apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ25_spl
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,definition,
( sQ26_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( ~ sQ26_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f316,plain,
( ~ sQ5_spl
| sQ26_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f299,f310,f313,f132]) ).
fof(f319,plain,
( ~ sQ25_spl
| distinct_points(sK2_skl,sK2_skl)
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f311,f29]) ).
fof(f323,definition,
( sQ27_spl
<=> distinct_points(sK2_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( ~ sQ27_spl
| distinct_points(sK2_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,plain,
( ~ sQ25_spl
| sQ27_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f319,f63,f323,f310]) ).
fof(f327,plain,
( ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f324,f15]) ).
fof(f328,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f327]) ).
fof(f329,plain,
( ~ sQ26_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f314,f30]) ).
fof(f333,plain,
( ~ sQ26_spl
| sQ16_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f329,f63,f192,f313]) ).
fof(f338,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f66,f141,f195,f208,f210,f212,f316,f326,f328,f333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:11:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.50 % Refutation found
% 0.13/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.52 % Elapsed time: 0.154384 seconds
% 0.13/0.52 % CPU time: 1.071715 seconds
% 0.13/0.52 % Total memory used: 26.886 MB
% 0.13/0.52 % Net memory used: 24.861 MB
%------------------------------------------------------------------------------