%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO190+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 : n005.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 0.15s 0.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 9 unt; 5 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 161 ( 61 ~; 73 |; 15 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 69 ( 66 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f13,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(f15,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,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)],[f15]) ).
fof(f17,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f42,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)],[f13]) ).
fof(f43,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,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)],[f43]) ).
fof(f48,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)],[f16]) ).
fof(f49,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)],[f48]) ).
fof(f50,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
apart_point_and_line(sK2_skl,line_connecting(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f56,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f54,f44]) ).
fof(f60,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)],[f56,f38]) ).
fof(f62,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X1,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK1_skl,sK0_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f60,f53]) ).
fof(f76,plain,
! [X0] :
( ~ distinct_points(sK1_skl,sK0_skl)
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK1_skl,sK0_skl))
| ~ distinct_points(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f62,f32]) ).
fof(f80,definition,
! [X0] :
( sQ0_spl
<=> ( apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK1_skl,sK0_skl))
| ~ distinct_points(X0,sK0_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK1_skl,sK0_skl))
| ~ distinct_points(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ1_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ1_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,definition,
( sQ2_spl
<=> distinct_points(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( ~ sQ2_spl
| distinct_points(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f88,plain,
( sQ2_spl
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f80,f83,f86]) ).
fof(f93,definition,
( sQ4_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ4_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f113,plain,
! [X0] :
( sQ2_spl
| distinct_points(X0,sK0_skl)
| ~ distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f88,f22]) ).
fof(f115,plain,
( sQ2_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f113,f17]) ).
fof(f116,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f50]) ).
fof(f117,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f126,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f81,f87]) ).
fof(f139,definition,
( sQ11_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ11_spl
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f126,f139,f93,f80,f86]) ).
fof(f152,plain,
( ~ sQ4_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f94,f32]) ).
fof(f155,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f50]) ).
fof(f156,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f157,plain,
( ~ sQ11_spl
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f140,f30]) ).
fof(f160,plain,
( ~ sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f157,f86,f139]) ).
fof(f161,plain,
( ~ sQ1_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f84,f30]) ).
fof(f164,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f50]) ).
fof(f165,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f166,plain,
$false,
inference(sat_refutation,[status(thm)],[f89,f117,f142,f156,f160,f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO190+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n005.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 20 13:14:03 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.15/0.51 % Refutation found
% 0.15/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.53 % Elapsed time: 0.092590 seconds
% 0.15/0.53 % CPU time: 0.314926 seconds
% 0.15/0.53 % Total memory used: 16.776 MB
% 0.15/0.53 % Net memory used: 16.251 MB
%------------------------------------------------------------------------------