%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO220+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 : n016.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 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 70 ( 31 ~; 21 |; 13 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 51 ( 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [L,M,N] :
( ( orthogonal_lines(L,N)
& orthogonal_lines(L,M) )
=> parallel_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [L,M,N] :
( ( orthogonal_lines(L,N)
& orthogonal_lines(L,M) )
=> parallel_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f96,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f97,plain,
! [M,N] :
( ~ convergent_lines(M,N)
| ! [L] :
( unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f115,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f116,plain,
( ! [X,Y] :
( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| parallel_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f123,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f124,plain,
( ! [X,Y] :
( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ! [X,Y] :
( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
? [L,M,N] :
( ~ parallel_lines(M,N)
& orthogonal_lines(L,N)
& orthogonal_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
? [M,N] :
( ~ parallel_lines(M,N)
& ? [L] :
( orthogonal_lines(L,N)
& orthogonal_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ~ parallel_lines(sK0_skl,sK1_skl)
& orthogonal_lines(sK2_skl,sK1_skl)
& orthogonal_lines(sK2_skl,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(L,sK2_skl)],[f128]) ).
fof(f130,plain,
orthogonal_lines(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
orthogonal_lines(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
~ parallel_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ~ orthogonal_lines(X0,X2)
| ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1) ),
inference(resolution,[status(thm)],[f98,f125]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ~ orthogonal_lines(X2,X0)
| ~ orthogonal_lines(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f150,f125]) ).
fof(f156,plain,
! [X0] :
( ~ orthogonal_lines(sK2_skl,X0)
| ~ convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f153,f131]) ).
fof(f160,plain,
~ convergent_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f156,f130]) ).
fof(f168,plain,
parallel_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f160,f118]) ).
fof(f169,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f168,f132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO220+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 : n016.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 13:47:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.049158 seconds
% 0.09/0.42 % CPU time: 0.159799 seconds
% 0.09/0.42 % Total memory used: 17.978 MB
% 0.09/0.42 % Net memory used: 17.862 MB
%------------------------------------------------------------------------------