%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO170+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:24:15 PM UTC 2026
% Result : Theorem 0.14s 0.55s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 7 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 121 ( 46 ~; 53 |; 15 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 63 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y,Z] :
( ( incident_point_and_line(Y,Z)
& incident_point_and_line(X,Z)
& distinct_points(X,Y) )
=> equal_lines(Z,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,Z] :
( ( incident_point_and_line(Y,Z)
& incident_point_and_line(X,Z)
& distinct_points(X,Y) )
=> equal_lines(Z,line_connecting(X,Y)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f50,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f51,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f58,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(f59,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)],[f58]) ).
fof(f111,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f112,plain,
( ! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ! [X,Y] :
( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f119,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f120,plain,
( ! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ! [X,Y] :
( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f127,plain,
? [X,Y,Z] :
( ~ equal_lines(Z,line_connecting(X,Y))
& incident_point_and_line(Y,Z)
& incident_point_and_line(X,Z)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ~ equal_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& incident_point_and_line(sK1_skl,sK2_skl)
& incident_point_and_line(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)],[f127]) ).
fof(f129,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
incident_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
incident_point_and_line(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f132,plain,
~ equal_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( equal_lines(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_points(X0,X1) ),
inference(resolution,[status(thm)],[f59,f114]) ).
fof(f161,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X1,sK2_skl)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f158,f132]) ).
fof(f166,plain,
! [X0,X1] :
( ~ incident_point_and_line(X1,sK2_skl)
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f161,f121]) ).
fof(f168,plain,
! [X0,X1] :
( ~ incident_point_and_line(X0,sK2_skl)
| ~ incident_point_and_line(X1,sK2_skl)
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f166,f121]) ).
fof(f169,plain,
! [X0] :
( ~ incident_point_and_line(X0,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f168,f131]) ).
fof(f172,plain,
! [X0] :
( ~ distinct_points(sK0_skl,sK1_skl)
| ~ incident_point_and_line(X0,sK2_skl)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f169,f53]) ).
fof(f175,plain,
! [X0] :
( ~ incident_point_and_line(X0,sK2_skl)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f129]) ).
fof(f224,plain,
( apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f175,f130]) ).
fof(f226,plain,
apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f224,f129]) ).
fof(f227,plain,
~ distinct_points(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f226,f51]) ).
fof(f231,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f227,f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO170+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.48 % Computer : n004.cluster.edu
% 0.14/0.48 % Model : x86_64 x86_64
% 0.14/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.48 % Memory : 8046.5625MB
% 0.14/0.48 % OS : Linux 6.8.0-71-generic
% 0.14/0.48 % CPULimit : 300
% 0.14/0.48 % WCLimit : 300
% 0.14/0.48 % DateTime : Sun Sep 20 12:52:34 UTC 2026
% 0.14/0.49 % CPUTime :
% 0.14/0.52 % Drodi V4.1.1
% 0.14/0.55 % Refutation found
% 0.14/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.59 % Elapsed time: 0.079755 seconds
% 0.20/0.59 % CPU time: 0.214761 seconds
% 0.20/0.59 % Total memory used: 11.406 MB
% 0.20/0.59 % Net memory used: 11.218 MB
%------------------------------------------------------------------------------