%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO234+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:24:39 PM UTC 2026
% Result : Theorem 0.16s 6.93s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 78 ( 32 ~; 33 |; 9 &)
% ( 0 <=>; 4 =>; 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 : 59 ( 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [L,M,N] :
( unequally_directed_lines(L,reverse_line(M))
=> ( unequally_directed_lines(M,reverse_line(N))
| unequally_directed_lines(L,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [L,M,N] :
( unequally_directed_lines(L,reverse_line(M))
=> ( unequally_directed_lines(M,reverse_line(N))
| unequally_directed_lines(L,N) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f78,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f79,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f80,plain,
! [L,M] :
( ! [N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) )
| ~ unequally_directed_lines(L,M) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f90,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)],[f14]) ).
fof(f91,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)],[f90]) ).
fof(f96,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f97,plain,
( ! [L,M] : ~ left_convergent_lines(L,reverse_line(M))
& ! [L,M] : ~ left_convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f130,plain,
? [L,M,N] :
( ~ unequally_directed_lines(M,reverse_line(N))
& ~ unequally_directed_lines(L,N)
& unequally_directed_lines(L,reverse_line(M)) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
? [L,M] :
( ? [N] :
( ~ unequally_directed_lines(M,reverse_line(N))
& ~ unequally_directed_lines(L,N) )
& unequally_directed_lines(L,reverse_line(M)) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
( ~ unequally_directed_lines(sK1_skl,reverse_line(sK2_skl))
& ~ unequally_directed_lines(sK0_skl,sK2_skl)
& unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl),skolemize(N,sK2_skl)],[f131]) ).
fof(f133,plain,
unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
~ unequally_directed_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
~ unequally_directed_lines(sK1_skl,reverse_line(sK2_skl)),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f147,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)],[f91,f98]) ).
fof(f152,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f98]) ).
fof(f153,plain,
! [X0] :
( unequally_directed_lines(reverse_line(sK1_skl),X0)
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f81,f133]) ).
fof(f154,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(reverse_line(sK1_skl),X1)
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f153,f81]) ).
fof(f156,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(reverse_line(sK1_skl),X2)
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f154,f81]) ).
fof(f159,plain,
! [X0,X1] :
( unequally_directed_lines(X1,reverse_line(sK1_skl))
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f156,f78]) ).
fof(f166,plain,
! [X0] :
( unequally_directed_lines(X0,reverse_line(sK1_skl))
| unequally_directed_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f159,f134]) ).
fof(f170,plain,
unequally_directed_lines(sK2_skl,reverse_line(sK1_skl)),
inference(resolution,[status(thm)],[f166,f78]) ).
fof(f171,plain,
! [X0] :
( unequally_directed_lines(reverse_line(sK1_skl),X0)
| unequally_directed_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f170,f81]) ).
fof(f195,plain,
unequally_directed_lines(reverse_line(sK1_skl),sK2_skl),
inference(resolution,[status(thm)],[f171,f78]) ).
fof(f216,plain,
! [X0,X1] :
( unequally_directed_lines(X1,reverse_line(X0))
| unequally_directed_lines(sK0_skl,X1)
| ~ unequally_directed_lines(reverse_line(sK1_skl),X0) ),
inference(resolution,[status(thm)],[f152,f154]) ).
fof(f218,plain,
~ unequally_directed_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f152,f133]) ).
fof(f241,plain,
! [X0] :
( unequally_directed_lines(sK1_skl,reverse_line(X0))
| ~ unequally_directed_lines(reverse_line(sK1_skl),X0) ),
inference(resolution,[status(thm)],[f216,f218]) ).
fof(f305,plain,
~ unequally_directed_lines(reverse_line(sK1_skl),sK2_skl),
inference(resolution,[status(thm)],[f241,f135]) ).
fof(f308,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f305,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO234+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/6.89 % Computer : n002.cluster.edu
% 0.11/6.89 % Model : x86_64 x86_64
% 0.11/6.89 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/6.89 % Memory : 8046.5625MB
% 0.11/6.89 % OS : Linux 6.8.0-71-generic
% 0.11/6.89 % CPULimit : 300
% 0.11/6.89 % WCLimit : 300
% 0.11/6.89 % DateTime : Sun Sep 20 14:14:31 UTC 2026
% 0.11/6.89 % CPUTime :
% 0.16/6.90 % Drodi V4.1.1
% 0.16/6.93 % Refutation found
% 0.16/6.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/6.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/6.96 % Elapsed time: 0.057746 seconds
% 0.16/6.96 % CPU time: 0.235522 seconds
% 0.16/6.96 % Total memory used: 13.537 MB
% 0.16/6.96 % Net memory used: 13.128 MB
%------------------------------------------------------------------------------