%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO262+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 : n018.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 12:24:46 PM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 4 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 105 ( 36 ~; 26 |; 38 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 72 ( 60 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L,M,N,A,B,C] :
( ( incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& incident_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L,M,N,A,B,C] :
( ( incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& incident_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f40,plain,
( ! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ! [X,Y] :
( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f64,plain,
! [L,M] :
( ( ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f65,plain,
( ! [L,M] :
( ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ! [L,M] :
( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f111,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f112,plain,
! [X0,X1] :
( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f117,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f118,plain,
( ! [L,M] : ~ left_convergent_lines(L,reverse_line(M))
& ! [L,M] : ~ left_convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f152,plain,
? [L,M,N,A,B,C] :
( ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C)))
& incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& incident_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
? [M,N,A,B,C] :
( ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C)))
& incident_point_and_line(B,N)
& convergent_lines(M,N)
& ? [L] :
( convergent_lines(L,N)
& incident_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
( ~ between_on_line(sK0_skl,intersection_point(sK0_skl,parallel_through_point(sK1_skl,sK2_skl)),sK3_skl,intersection_point(sK0_skl,parallel_through_point(sK1_skl,sK4_skl)))
& incident_point_and_line(sK3_skl,sK1_skl)
& convergent_lines(sK0_skl,sK1_skl)
& convergent_lines(sK5_skl,sK1_skl)
& incident_point_and_line(sK3_skl,sK0_skl)
& convergent_lines(sK5_skl,sK0_skl)
& between_on_line(sK5_skl,sK2_skl,sK3_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(L,sK5_skl)],[f153]) ).
fof(f159,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f172,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f112,f119]) ).
fof(f178,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f119]) ).
fof(f236,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f178,f41]) ).
fof(f241,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f236,f67]) ).
fof(f245,plain,
! [X0,X1] : ~ convergent_lines(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f241,f66]) ).
fof(f246,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f159,f245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO262+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 14:51:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.052713 seconds
% 0.08/0.42 % CPU time: 0.194400 seconds
% 0.08/0.42 % Total memory used: 13.438 MB
% 0.08/0.42 % Net memory used: 13.315 MB
%------------------------------------------------------------------------------