%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO267+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 : n006.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 12:24:47 PM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 35 ( 14 ~; 10 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 28 ( 22 !; 6 ?)
% 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(f18,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L,M,N] :
( unequally_directed_opposite_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_opposite_lines(M,N) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L,M,N] :
( unequally_directed_opposite_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_opposite_lines(M,N) ) ),
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(f42,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f110,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f152,plain,
? [L,M,N] :
( ~ unequally_directed_lines(M,N)
& ~ unequally_directed_opposite_lines(M,N)
& unequally_directed_opposite_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
? [M] :
( ? [N] :
( ~ unequally_directed_lines(M,N)
& ~ unequally_directed_opposite_lines(M,N) )
& ? [L] : unequally_directed_opposite_lines(L,M) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
( ~ unequally_directed_lines(sK0_skl,sK2_skl)
& ~ unequally_directed_opposite_lines(sK0_skl,sK2_skl)
& unequally_directed_opposite_lines(sK1_skl,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(M,sK0_skl),skolemize(L,sK1_skl),skolemize(N,sK2_skl)],[f153]) ).
fof(f156,plain,
~ unequally_directed_opposite_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f157,plain,
~ unequally_directed_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f200,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f110,f42]) ).
fof(f210,plain,
unequally_directed_opposite_lines(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f200,f157]) ).
fof(f214,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f210,f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO267+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 14:56:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.044612 seconds
% 0.11/0.42 % CPU time: 0.132405 seconds
% 0.11/0.42 % Total memory used: 14.671 MB
% 0.11/0.42 % Net memory used: 14.567 MB
%------------------------------------------------------------------------------