%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO181+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 : n011.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 0.09s 0.49s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 9 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 161 ( 53 ~; 89 |; 10 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 93 ( 87 !; 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,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(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/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] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(Y,line_connecting(X,Z)) ) ),
file('/export/starexec/sandbox2/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(Y,line_connecting(X,Z)) ) ),
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(Y,line_connecting(X,Z))
& 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(Y,line_connecting(X,Z))
& 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(sK1_skl,line_connecting(sK0_skl,sK2_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(sK1_skl,line_connecting(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
( distinct_points(sK2_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f29,f49]) ).
fof(f52,plain,
distinct_points(sK2_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f51,f48]) ).
fof(f58,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(f59,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X1,X0)
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X1,X2)
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f58,f36]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( distinct_points(sK2_skl,X3)
| ~ distinct_points(X2,X3)
| apart_point_and_line(X1,line_connecting(X2,X3))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(X2,X3))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f59,f30]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ distinct_points(X2,sK2_skl)
| apart_point_and_line(X1,line_connecting(X2,sK2_skl))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(X2,sK2_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f86,f15]) ).
fof(f123,plain,
! [X0,X1,X2] :
( distinct_points(X1,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl)
| ~ distinct_points(X2,sK2_skl)
| apart_point_and_line(X1,line_connecting(X2,sK2_skl))
| apart_point_and_line(X0,line_connecting(X2,sK2_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f93,f30]) ).
fof(f127,plain,
! [X0,X1,X2] :
( distinct_points(X1,sK1_skl)
| ~ distinct_points(X2,sK2_skl)
| apart_point_and_line(X1,line_connecting(X2,sK2_skl))
| apart_point_and_line(X0,line_connecting(X2,sK2_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f48]) ).
fof(f129,plain,
! [X0,X1] :
( ~ distinct_points(X1,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(X1,sK2_skl))
| apart_point_and_line(X0,line_connecting(X1,sK2_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f127,f15]) ).
fof(f131,plain,
! [X0,X1] :
( distinct_points(X0,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl)
| ~ distinct_points(X1,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(X1,sK2_skl))
| apart_point_and_line(X0,line_connecting(X1,sK2_skl))
| ~ distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f129,f29]) ).
fof(f134,plain,
! [X0,X1] :
( distinct_points(X0,sK0_skl)
| ~ distinct_points(X1,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(X1,sK2_skl))
| apart_point_and_line(X0,line_connecting(X1,sK2_skl))
| ~ distinct_points(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f48]) ).
fof(f176,plain,
! [X0] :
( ~ distinct_points(X0,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(X0,sK2_skl))
| apart_point_and_line(sK0_skl,line_connecting(X0,sK2_skl))
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f134,f15]) ).
fof(f177,plain,
! [X0] :
( ~ distinct_points(X0,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(X0,sK2_skl))
| apart_point_and_line(sK0_skl,line_connecting(X0,sK2_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f48]) ).
fof(f179,plain,
! [X0] :
( distinct_points(sK0_skl,X0)
| ~ distinct_points(X0,sK2_skl)
| ~ distinct_points(X0,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(X0,sK2_skl)) ),
inference(resolution,[status(thm)],[f177,f29]) ).
fof(f183,plain,
! [X0] :
( distinct_points(sK0_skl,X0)
| ~ distinct_points(X0,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(X0,sK2_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f179]) ).
fof(f188,plain,
( ~ distinct_points(sK0_skl,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f183,f15]) ).
fof(f189,plain,
~ distinct_points(sK0_skl,sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f188,f50]) ).
fof(f192,plain,
! [X0] :
( distinct_points(X0,sK2_skl)
| ~ distinct_points(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f189,f20]) ).
fof(f194,plain,
~ distinct_points(sK2_skl,sK0_skl),
inference(resolution,[status(thm)],[f192,f15]) ).
fof(f195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f194,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO181+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:03:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.49 % Refutation found
% 0.09/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.51 % Elapsed time: 0.136353 seconds
% 0.09/0.51 % CPU time: 0.867998 seconds
% 0.09/0.51 % Total memory used: 23.581 MB
% 0.09/0.51 % Net memory used: 22.263 MB
%------------------------------------------------------------------------------