%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO205+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 : n010.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 12:24:29 PM UTC 2026
% Result : Theorem 0.14s 10.52s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 17 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 66 ~; 68 |; 13 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 140 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
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(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
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(f36,conjecture,
! [X,Y,Z] :
( ( equal_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( equal_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,Z] :
( ( equal_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( equal_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f47,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f48,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
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(f63,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(f64,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,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)],[f64]) ).
fof(f66,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f67,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f72,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f107,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f108,plain,
( ! [X,Y] :
( distinct_points(X,Y)
| equal_points(X,Y) )
& ! [X,Y] :
( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f110,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
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(f113,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| ~ equal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f127,plain,
? [X,Y,Z] :
( ( ~ equal_points(intersection_point(X,Y),intersection_point(X,Z))
| ~ convergent_lines(X,Z) )
& equal_lines(Y,Z)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ( ~ equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))
| ~ convergent_lines(sK0_skl,sK2_skl) )
& equal_lines(sK1_skl,sK2_skl)
& convergent_lines(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,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
equal_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
( ~ equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f142,plain,
( ~ convergent_lines(sK0_skl,sK2_skl)
| distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f110,f131]) ).
fof(f144,plain,
~ distinct_lines(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f113,f130]) ).
fof(f146,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f49,f40]) ).
fof(f148,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[status(thm)],[f71,f146]) ).
fof(f149,plain,
! [X0,X1,X2] :
( convergent_lines(X2,X0)
| ~ convergent_lines(parallel_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f71,f49]) ).
fof(f151,plain,
! [X0,X1,X2] :
( convergent_lines(X1,parallel_through_point(X0,X2))
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f148,f49]) ).
fof(f153,plain,
! [X0,X1,X2] : ~ convergent_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0),
inference(resolution,[status(thm)],[f149,f148]) ).
fof(f160,plain,
! [X0,X1] : ~ distinct_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[status(thm)],[f70,f148]) ).
fof(f215,plain,
! [X0,X1,X2,X3] : ~ convergent_lines(X0,parallel_through_point(parallel_through_point(parallel_through_point(X0,X1),X2),X3)),
inference(resolution,[status(thm)],[f151,f153]) ).
fof(f411,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,parallel_through_point(X1,X2))
| ~ apart_point_and_line(X0,X1) ),
inference(resolution,[status(thm)],[f65,f160]) ).
fof(f435,plain,
! [X0,X1] : ~ apart_point_and_line(X0,X1),
inference(resolution,[status(thm)],[f411,f72]) ).
fof(f438,plain,
! [X0,X1,X2,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(backward_subsumption_resolution,[status(thm)],[f59,f435]) ).
fof(f442,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f435]) ).
fof(f460,plain,
! [X0] :
( convergent_lines(X0,sK2_skl)
| ~ convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f68,f144]) ).
fof(f578,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f435]) ).
fof(f579,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f578,f435]) ).
fof(f591,plain,
! [X0,X1,X2,X3,X4] :
( convergent_lines(X2,X4)
| ~ convergent_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f579,f68]) ).
fof(f757,plain,
! [X0,X1,X2,X3] :
( ~ convergent_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f591,f215]) ).
fof(f761,plain,
~ convergent_lines(sK0_skl,sK2_skl),
inference(backward_subsumption_resolution,[status(thm)],[f142,f757]) ).
fof(f783,plain,
~ convergent_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f761,f460]) ).
fof(f791,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f783,f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n010.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sun Sep 20 13:26:50 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.38 % Drodi V4.1.1
% 0.14/10.52 % Refutation found
% 0.14/10.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.54 % Elapsed time: 0.154484 seconds
% 0.14/10.54 % CPU time: 0.978989 seconds
% 0.14/10.54 % Total memory used: 28.164 MB
% 0.14/10.54 % Net memory used: 26.121 MB
%------------------------------------------------------------------------------