%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO221+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 12:24:35 PM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 99 ( 41 ~; 46 |; 4 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 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 : 96 ( 93 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A,B,L] :
( incident_point_and_line(B,orthogonal_through_point(L,A))
=> equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A,B,L] :
( incident_point_and_line(B,orthogonal_through_point(L,A))
=> equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f39,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f44,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f54,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f55,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
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(f83,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f85,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f86,plain,
! [L,M] :
( ! [N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| ! [A] :
( apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) )
| ~ distinct_lines(L,M) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
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(f127,plain,
? [A,B,L] :
( ~ equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B))
& incident_point_and_line(B,orthogonal_through_point(L,A)) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ~ equal_lines(orthogonal_through_point(sK2_skl,sK0_skl),orthogonal_through_point(sK2_skl,sK1_skl))
& incident_point_and_line(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(L,sK2_skl)],[f127]) ).
fof(f130,plain,
~ equal_lines(orthogonal_through_point(sK2_skl,sK0_skl),orthogonal_through_point(sK2_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f143,plain,
! [X0,X1,X2] :
( equal_lines(X0,X2)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f46,f114]) ).
fof(f144,plain,
! [X0] :
( distinct_lines(orthogonal_through_point(sK2_skl,sK1_skl),X0)
| distinct_lines(orthogonal_through_point(sK2_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f143,f130]) ).
fof(f146,plain,
distinct_lines(orthogonal_through_point(sK2_skl,sK0_skl),orthogonal_through_point(sK2_skl,sK1_skl)),
inference(resolution,[status(thm)],[f144,f39]) ).
fof(f198,plain,
! [X0,X1,X2,X3] :
( unorthogonal_lines(X0,X1)
| apart_point_and_line(X3,orthogonal_through_point(X1,X2))
| apart_point_and_line(X3,X0)
| ~ distinct_lines(X0,orthogonal_through_point(X1,X2)) ),
inference(resolution,[status(thm)],[f87,f83]) ).
fof(f213,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X3,orthogonal_through_point(X0,X2))
| apart_point_and_line(X3,orthogonal_through_point(X0,X1))
| ~ distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2)) ),
inference(resolution,[status(thm)],[f198,f83]) ).
fof(f215,plain,
! [X0,X1,X2,X3] :
( ~ convergent_lines(X3,orthogonal_through_point(X0,X2))
| apart_point_and_line(intersection_point(X3,orthogonal_through_point(X0,X2)),orthogonal_through_point(X0,X1))
| ~ distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2)) ),
inference(resolution,[status(thm)],[f213,f57]) ).
fof(f244,plain,
! [X0,X1,X2] :
( ~ convergent_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2))
| ~ convergent_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2))
| ~ distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2)) ),
inference(resolution,[status(thm)],[f215,f55]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ~ convergent_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2))
| ~ distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f244]) ).
fof(f252,plain,
! [X0,X1,X2] : ~ distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2)),
inference(forward_subsumption_resolution,[status(thm)],[f250,f70]) ).
fof(f253,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f146,f252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO221+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.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 13:45:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.43 % Refutation found
% 0.09/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.069273 seconds
% 0.09/0.45 % CPU time: 0.365809 seconds
% 0.09/0.45 % Total memory used: 21.273 MB
% 0.09/0.45 % Net memory used: 20.685 MB
%------------------------------------------------------------------------------