%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO182+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 : n009.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 12:24:20 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 8 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 133 ( 57 ~; 60 |; 7 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 81 !; 6 ?)
% 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] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(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] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(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(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
? [X,Y] :
( ? [Z] :
( ~ apart_point_and_line(Z,line_connecting(Y,X))
& apart_point_and_line(Z,line_connecting(X,Y)) )
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,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(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)],[f49]) ).
fof(f51,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
~ apart_point_and_line(sK2_skl,line_connecting(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,plain,
! [X0,X1] :
( distinct_points(X1,X0)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f22,f17]) ).
fof(f81,plain,
! [X0] :
( distinct_lines(X0,line_connecting(sK1_skl,sK0_skl))
| ~ apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f44,f53]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( ~ distinct_points(X2,X0)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,line_connecting(X2,X0))
| apart_point_and_line(X0,X3)
| ~ distinct_lines(line_connecting(X2,X0),X3)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f38,f32]) ).
fof(f233,plain,
! [X0,X1,X2] :
( ~ distinct_points(X1,X0)
| ~ distinct_points(X1,X0)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(line_connecting(X1,X0),X2)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f98,f30]) ).
fof(f245,plain,
! [X0,X1,X2] :
( ~ distinct_points(X1,X0)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(line_connecting(X1,X0),X2)
| ~ distinct_points(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f233]) ).
fof(f246,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2)
| ~ distinct_lines(line_connecting(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f55]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ~ distinct_points(X1,X2)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,line_connecting(X1,X2))
| ~ distinct_lines(line_connecting(X0,X1),line_connecting(X1,X2)) ),
inference(resolution,[status(thm)],[f246,f30]) ).
fof(f283,plain,
! [X0,X1] :
( ~ distinct_points(X1,X0)
| ~ distinct_points(X1,X0)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(resolution,[status(thm)],[f256,f32]) ).
fof(f285,plain,
! [X0,X1] :
( ~ distinct_points(X1,X0)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f283]) ).
fof(f286,plain,
! [X0,X1] :
( ~ distinct_points(X1,X0)
| ~ distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f55]) ).
fof(f288,plain,
( ~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f286,f81]) ).
fof(f301,plain,
~ distinct_points(sK1_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f288,f52]) ).
fof(f372,plain,
~ distinct_points(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f301,f55]) ).
fof(f377,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f372,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO182+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 13:06:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.056874 seconds
% 0.09/0.43 % CPU time: 0.222452 seconds
% 0.09/0.43 % Total memory used: 18.867 MB
% 0.09/0.43 % Net memory used: 18.241 MB
%------------------------------------------------------------------------------