%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO231+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 : n010.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 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 11 unt; 1 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 128 ( 52 ~; 51 |; 17 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 95 ( 89 !; 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(f4,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,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(f18,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L,M,N] :
( ( equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) )
=> equally_directed_opposite_lines(M,N) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L,M,N] :
( ( equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) )
=> equally_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(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(f51,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f52,plain,
( ! [X,Y] :
( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ! [X,Y] :
( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f56,plain,
( ! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ! [X,Y] :
( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f101,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)],[f16]) ).
fof(f102,plain,
! [L,M] :
( ! [N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) )
| ~ unequally_directed_lines(L,M) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
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,N] :
( ~ equally_directed_opposite_lines(M,N)
& equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
? [M,N] :
( ~ equally_directed_opposite_lines(M,N)
& ? [L] :
( equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
( ~ equally_directed_opposite_lines(sK0_skl,sK1_skl)
& equally_directed_lines(sK2_skl,sK1_skl)
& equally_directed_opposite_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)],[f153]) ).
fof(f155,plain,
equally_directed_opposite_lines(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f156,plain,
equally_directed_lines(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f157,plain,
~ equally_directed_opposite_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f163,plain,
unequally_directed_opposite_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f58,f157]) ).
fof(f165,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(resolution,[status(thm)],[f41,f53]) ).
fof(f168,plain,
~ equally_directed_lines(sK0_skl,reverse_line(sK1_skl)),
inference(resolution,[status(thm)],[f165,f163]) ).
fof(f169,plain,
unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)),
inference(resolution,[status(thm)],[f168,f54]) ).
fof(f174,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f110,f42]) ).
fof(f242,plain,
! [X0,X1,X2] :
( unequally_directed_opposite_lines(X0,X2)
| unequally_directed_lines(X2,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f103,f174]) ).
fof(f303,plain,
! [X0,X1,X2] :
( ~ equally_directed_lines(X2,X1)
| unequally_directed_opposite_lines(X2,X0)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f242,f53]) ).
fof(f314,plain,
! [X0] :
( unequally_directed_opposite_lines(sK2_skl,X0)
| unequally_directed_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f303,f156]) ).
fof(f467,definition,
( sQ12_spl
<=> unequally_directed_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ12_spl
| unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f469,plain,
( sQ12_spl
| ~ unequally_directed_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f528,plain,
! [X0,X1] :
( left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f119]) ).
fof(f529,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f528,f119]) ).
fof(f532,plain,
( sQ12_spl
| unequally_directed_opposite_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f469,f314]) ).
fof(f647,plain,
( sQ12_spl
| ~ equally_directed_opposite_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f532,f57]) ).
fof(f648,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f647,f155]) ).
fof(f649,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f648]) ).
fof(f739,plain,
~ unequally_directed_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f529,f169]) ).
fof(f766,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f739,f468]) ).
fof(f767,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f766]) ).
fof(f768,plain,
$false,
inference(sat_refutation,[status(thm)],[f649,f767]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.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 14:08:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.43 % Refutation found
% 0.09/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.46 % Elapsed time: 0.077148 seconds
% 0.09/0.46 % CPU time: 0.393992 seconds
% 0.09/0.46 % Total memory used: 22.709 MB
% 0.09/0.46 % Net memory used: 22.234 MB
%------------------------------------------------------------------------------