%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO255+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 : n026.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 12:24:44 PM UTC 2026
% Result : Theorem 0.13s 5.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 10 unt; 2 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 116 ( 50 ~; 43 |; 17 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 79 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [L] : equally_directed_lines(L,L),
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(f30,axiom,
! [A,B] :
( distinct_points(A,B)
=> equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L,A,B] :
~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L,A,B] :
~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
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(f77,plain,
! [L,A,B] :
( ( ~ equally_directed_lines(L,line_connecting(A,B))
| ~ incident_point_and_line(B,L)
| ~ incident_point_and_line(A,L)
| ~ distinct_points(A,B)
| before_on_line(L,A,B) )
& ( ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f78,plain,
( ! [L,A,B] :
( ~ equally_directed_lines(L,line_connecting(A,B))
| ~ incident_point_and_line(B,L)
| ~ incident_point_and_line(A,L)
| ~ distinct_points(A,B)
| before_on_line(L,A,B) )
& ! [L,A,B] :
( ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
! [X0,X1,X2] :
( equally_directed_lines(X0,line_connecting(X1,X2))
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f100,plain,
! [X0] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
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(f137,plain,
! [A,B] :
( equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))
| ~ distinct_points(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f138,plain,
! [X0,X1] :
( equally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0)))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f152,plain,
? [L,A,B] :
( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
( before_on_line(sK0_skl,sK2_skl,sK1_skl)
& before_on_line(sK0_skl,sK1_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(L,sK0_skl),skolemize(A,sK1_skl),skolemize(B,sK2_skl)],[f152]) ).
fof(f154,plain,
before_on_line(sK0_skl,sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
before_on_line(sK0_skl,sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,line_connecting(X1,X2))
| ~ before_on_line(X0,X1,X2) ),
inference(resolution,[status(thm)],[f82,f53]) ).
fof(f169,plain,
! [X0,X1] :
( ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0)))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f138,f53]) ).
fof(f174,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(resolution,[status(thm)],[f100,f53]) ).
fof(f177,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| unequally_directed_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(resolution,[status(thm)],[f110,f169]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ~ before_on_line(X2,X0,X1)
| unequally_directed_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(resolution,[status(thm)],[f177,f79]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( ~ before_on_line(X1,X2,X3)
| unequally_directed_lines(X0,line_connecting(X2,X3))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f103,f167]) ).
fof(f232,plain,
! [X0] :
( unequally_directed_lines(X0,line_connecting(sK2_skl,sK1_skl))
| ~ unequally_directed_lines(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f191,f155]) ).
fof(f233,plain,
! [X0] :
( unequally_directed_lines(X0,line_connecting(sK1_skl,sK2_skl))
| ~ unequally_directed_lines(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f191,f154]) ).
fof(f281,plain,
~ unequally_directed_lines(line_connecting(sK2_skl,sK1_skl),sK0_skl),
inference(resolution,[status(thm)],[f232,f174]) ).
fof(f315,plain,
~ unequally_directed_lines(line_connecting(sK1_skl,sK2_skl),sK0_skl),
inference(resolution,[status(thm)],[f233,f174]) ).
fof(f337,plain,
! [X0] :
( unequally_directed_lines(X0,sK0_skl)
| ~ unequally_directed_lines(X0,line_connecting(sK2_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f281,f103]) ).
fof(f473,plain,
! [X0] :
( ~ before_on_line(X0,sK1_skl,sK2_skl)
| unequally_directed_lines(line_connecting(sK1_skl,sK2_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f337,f180]) ).
fof(f479,definition,
( sQ2_spl
<=> unequally_directed_lines(line_connecting(sK1_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( ~ sQ2_spl
| unequally_directed_lines(line_connecting(sK1_skl,sK2_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,definition,
! [X0] :
( sQ3_spl
<=> ~ before_on_line(X0,sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f483,plain,
! [X0] :
( ~ sQ3_spl
| ~ before_on_line(X0,sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f473,f479,f482]) ).
fof(f486,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f315]) ).
fof(f487,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f509,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f154,f483]) ).
fof(f510,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f511,plain,
$false,
inference(sat_refutation,[status(thm)],[f485,f487,f510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO255+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 14:40:26 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.13/5.45 % Refutation found
% 0.13/5.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.47 % Elapsed time: 0.083579 seconds
% 0.13/5.47 % CPU time: 0.506143 seconds
% 0.13/5.47 % Total memory used: 24.082 MB
% 0.13/5.47 % Net memory used: 23.232 MB
%------------------------------------------------------------------------------