%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO231+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:24:38 PM UTC 2026
% Result : Theorem 0.17s 0.56s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 11 unt; 2 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 93 ( 45 ~; 31 |; 11 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 50 ( 44 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [L,M,N] :
( ( ~ unequally_directed_lines(L,N)
& ~ unequally_directed_lines(L,reverse_line(M)) )
=> ~ unequally_directed_lines(M,reverse_line(N)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [L,M,N] :
( ( ~ unequally_directed_lines(L,N)
& ~ unequally_directed_lines(L,reverse_line(M)) )
=> ~ unequally_directed_lines(M,reverse_line(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,
? [M,N] :
( unequally_directed_lines(M,reverse_line(N))
& ? [L] :
( ~ unequally_directed_lines(L,N)
& ~ unequally_directed_lines(L,reverse_line(M)) ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
( unequally_directed_lines(sK0_skl,reverse_line(sK1_skl))
& ~ unequally_directed_lines(sK2_skl,sK1_skl)
& ~ unequally_directed_lines(sK2_skl,reverse_line(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)],[f131]) ).
fof(f133,plain,
~ unequally_directed_lines(sK2_skl,reverse_line(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
~ unequally_directed_lines(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
unequally_directed_lines(sK0_skl,reverse_line(sK1_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,f135]) ).
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(f158,plain,
unequally_directed_lines(reverse_line(sK1_skl),sK0_skl),
inference(resolution,[status(thm)],[f154,f78]) ).
fof(f164,plain,
( unequally_directed_lines(reverse_line(sK1_skl),reverse_line(sK0_skl))
| unequally_directed_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f154,f133]) ).
fof(f182,definition,
( sQ4_spl
<=> unequally_directed_lines(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ4_spl
| unequally_directed_lines(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ5_spl
<=> unequally_directed_lines(reverse_line(sK1_skl),reverse_line(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ5_spl
| unequally_directed_lines(reverse_line(sK1_skl),reverse_line(sK0_skl)) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f164,f182,f185]) ).
fof(f193,plain,
! [X0] :
( ~ sQ4_spl
| unequally_directed_lines(sK2_skl,X0)
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f183,f81]) ).
fof(f196,plain,
( ~ sQ4_spl
| unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f193,f134]) ).
fof(f251,plain,
~ unequally_directed_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f152,f135]) ).
fof(f253,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f251,f196]) ).
fof(f254,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ5_spl
| ~ unequally_directed_lines(reverse_line(sK1_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f186,f152]) ).
fof(f258,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f158]) ).
fof(f259,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f260,plain,
$false,
inference(sat_refutation,[status(thm)],[f188,f254,f259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO231+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 % Computer : n020.cluster.edu
% 0.17/0.47 % Model : x86_64 x86_64
% 0.17/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.47 % Memory : 8046.5625MB
% 0.17/0.47 % OS : Linux 6.8.0-71-generic
% 0.17/0.47 % CPULimit : 300
% 0.17/0.47 % WCLimit : 300
% 0.17/0.47 % DateTime : Sun Sep 20 14:07:17 UTC 2026
% 0.17/0.47 % CPUTime :
% 0.17/0.48 % Drodi V4.1.1
% 0.17/0.56 % Refutation found
% 0.17/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.60 % Elapsed time: 0.109149 seconds
% 0.21/0.60 % CPU time: 0.622640 seconds
% 0.21/0.60 % Total memory used: 22.659 MB
% 0.21/0.60 % Net memory used: 21.551 MB
%------------------------------------------------------------------------------