%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO201+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 : n026.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 12:24:28 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 19 unt; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 123 ( 52 ~; 58 |; 5 &)
% ( 1 <=>; 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; 2 con; 0-2 aty)
% Number of variables : 137 ( 135 !; 2 ?)
% 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(f19,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
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(f36,conjecture,
! [X,Y] :
( convergent_lines(X,Y)
=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y] :
( convergent_lines(X,Y)
=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ),
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(f76,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f83,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
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(f127,plain,
? [X,Y] :
( ~ equal_points(intersection_point(X,Y),intersection_point(Y,X))
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ~ equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl))
& convergent_lines(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f127]) ).
fof(f130,plain,
~ equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f141,plain,
distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl)),
inference(resolution,[status(thm)],[f110,f130]) ).
fof(f143,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f49,f40]) ).
fof(f145,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[status(thm)],[f71,f143]) ).
fof(f146,plain,
! [X0,X1,X2] :
( convergent_lines(X2,X0)
| ~ convergent_lines(parallel_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f71,f49]) ).
fof(f148,plain,
! [X0,X1,X2] :
( convergent_lines(X1,parallel_through_point(X0,X2))
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f145,f49]) ).
fof(f150,plain,
! [X0,X1,X2] : ~ convergent_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0),
inference(resolution,[status(thm)],[f146,f145]) ).
fof(f161,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)],[f148,f150]) ).
fof(f176,plain,
! [X0,X1] : ~ distinct_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[status(thm)],[f70,f145]) ).
fof(f178,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[f76,f83]) ).
fof(f290,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,f176]) ).
fof(f308,plain,
! [X0,X1] : ~ apart_point_and_line(X0,X1),
inference(resolution,[status(thm)],[f290,f72]) ).
fof(f309,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,f308]) ).
fof(f311,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)],[f309,f308]) ).
fof(f328,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)],[f311,f308]) ).
fof(f329,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f328,f308]) ).
fof(f330,plain,
! [X0,X1] : ~ distinct_lines(X0,X1),
inference(resolution,[status(thm)],[f329,f141]) ).
fof(f339,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f68,f330]) ).
fof(f347,plain,
! [X0,X1] : ~ convergent_lines(X0,X1),
inference(resolution,[status(thm)],[f339,f161]) ).
fof(f354,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f178,f347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 13:29:37 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.46 % Elapsed time: 0.087472 seconds
% 0.13/0.46 % CPU time: 0.489702 seconds
% 0.13/0.46 % Total memory used: 22.730 MB
% 0.13/0.46 % Net memory used: 21.771 MB
%------------------------------------------------------------------------------