%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO268+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 : n011.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 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 2 unt; 2 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 42 ~; 40 |; 7 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 46 ( 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L,M] :
( unequally_directed_lines(L,M)
<=> unequally_directed_opposite_lines(L,reverse_line(M)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L,M] :
( unequally_directed_lines(L,M)
<=> unequally_directed_opposite_lines(L,reverse_line(M)) ),
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(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(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] :
( unequally_directed_lines(L,M)
<~> unequally_directed_opposite_lines(L,reverse_line(M)) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
? [L,M] :
( ( ~ unequally_directed_opposite_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) )
& ( unequally_directed_opposite_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ) ),
inference(NNF_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
( ( ~ unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))
| ~ unequally_directed_lines(sK0_skl,sK1_skl) )
& ( unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))
| unequally_directed_lines(sK0_skl,sK1_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl)],[f153]) ).
fof(f155,plain,
( unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))
| unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))
| ~ unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f162,definition,
( sQ0_spl
<=> unequally_directed_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ0_spl
| ~ unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ1_spl
<=> unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ1_spl
| unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl)) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f167,plain,
( sQ1_spl
| ~ unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl)) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f155,f162,f165]) ).
fof(f169,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f156,f162,f165]) ).
fof(f175,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(f181,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f119]) ).
fof(f261,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f181,f41]) ).
fof(f286,plain,
( ~ sQ1_spl
| ~ unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)) ),
inference(resolution,[status(thm)],[f261,f166]) ).
fof(f296,plain,
( ~ sQ1_spl
| unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f286,f110]) ).
fof(f299,plain,
( ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f164]) ).
fof(f300,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( sQ1_spl
| ~ unequally_directed_lines(sK0_skl,reverse_line(reverse_line(sK1_skl))) ),
inference(resolution,[status(thm)],[f167,f42]) ).
fof(f311,plain,
( sQ1_spl
| unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)) ),
inference(resolution,[status(thm)],[f302,f110]) ).
fof(f321,plain,
( sQ1_spl
| ~ unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f311,f181]) ).
fof(f322,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f321,f162,f165]) ).
fof(f323,plain,
$false,
inference(sat_refutation,[status(thm)],[f168,f169,f300,f322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO268+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 14:57:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.084341 seconds
% 0.13/0.45 % CPU time: 0.428718 seconds
% 0.13/0.45 % Total memory used: 23.309 MB
% 0.13/0.45 % Net memory used: 22.313 MB
%------------------------------------------------------------------------------