%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO179+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 6 unt; 5 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 101 ( 39 ~; 41 |; 11 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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)],[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(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] :
( ( ~ 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)],[f14]) ).
fof(f46,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)],[f45]) ).
fof(f47,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,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)],[f46]) ).
fof(f50,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(f52,plain,
( sQ0_spl
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,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(f55,plain,
( sQ1_spl
| ~ distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f50,f53]) ).
fof(f60,plain,
( distinct_points(sK2_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f29,f48]) ).
fof(f61,definition,
( sQ2_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( sQ2_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ3_spl
<=> distinct_points(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ3_spl
| distinct_points(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f60,f61,f64]) ).
fof(f68,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f47]) ).
fof(f69,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f68]) ).
fof(f70,plain,
( distinct_points(sK2_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f30,f48]) ).
fof(f71,definition,
( sQ4_spl
<=> distinct_points(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ4_spl
| distinct_points(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f70,f61,f71]) ).
fof(f77,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f42,f48]) ).
fof(f79,plain,
! [X0,X1] :
( distinct_points(sK2_skl,X0)
| ~ distinct_points(X0,X1)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(X0,X1)) ),
inference(resolution,[status(thm)],[f77,f29]) ).
fof(f88,plain,
! [X0] :
( ~ distinct_points(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f79,f15]) ).
fof(f99,plain,
( sQ0_spl
| ~ distinct_points(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f88,f52]) ).
fof(f102,plain,
( sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f65]) ).
fof(f103,plain,
( sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f102]) ).
fof(f104,plain,
( sQ1_spl
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f55,f88]) ).
fof(f105,plain,
( sQ1_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f72]) ).
fof(f106,plain,
( sQ1_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f107,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f67,f69,f74,f103,f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO179+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n020.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 20 13:04:03 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.51 % Elapsed time: 0.083545 seconds
% 0.15/0.51 % CPU time: 0.082555 seconds
% 0.15/0.51 % Total memory used: 2.348 MB
% 0.15/0.51 % Net memory used: 2.319 MB
%------------------------------------------------------------------------------