%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO238+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 : 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 12:24:40 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 5 unt; 2 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 71 ( 26 ~; 20 |; 20 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 41 ( 33 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,L] :
( divides_points(L,A,B)
<=> ( ( left_apart_point(B,L)
& left_apart_point(A,reverse_line(L)) )
| ( left_apart_point(B,reverse_line(L))
& left_apart_point(A,L) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B,C,L] :
( ( divides_points(L,A,C)
& divides_points(L,A,B) )
=> ~ divides_points(L,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B,C,L] :
( ( divides_points(L,A,C)
& divides_points(L,A,B) )
=> ~ divides_points(L,B,C) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f44,plain,
! [A,B,L] :
( ( ( ( ~ left_apart_point(B,L)
| ~ left_apart_point(A,reverse_line(L)) )
& ( ~ left_apart_point(B,reverse_line(L))
| ~ left_apart_point(A,L) ) )
| divides_points(L,A,B) )
& ( ( left_apart_point(B,L)
& left_apart_point(A,reverse_line(L)) )
| ( left_apart_point(B,reverse_line(L))
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f45,plain,
( ! [A,B,L] :
( ( ( ~ left_apart_point(B,L)
| ~ left_apart_point(A,reverse_line(L)) )
& ( ~ left_apart_point(B,reverse_line(L))
| ~ left_apart_point(A,L) ) )
| divides_points(L,A,B) )
& ! [A,B,L] :
( ( left_apart_point(B,L)
& left_apart_point(A,reverse_line(L)) )
| ( left_apart_point(B,reverse_line(L))
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f47,plain,
! [X0,X1,X2] :
( left_apart_point(X2,X0)
| left_apart_point(X1,X0)
| ~ divides_points(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f92,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f93,plain,
( ! [A,L] : ~ left_apart_point(A,reverse_line(L))
& ! [A,L] : ~ left_apart_point(A,L) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f130,plain,
? [A,B,C,L] :
( divides_points(L,B,C)
& divides_points(L,A,C)
& divides_points(L,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
? [B,C,L] :
( divides_points(L,B,C)
& ? [A] :
( divides_points(L,A,C)
& divides_points(L,A,B) ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
( divides_points(sK2_skl,sK0_skl,sK1_skl)
& divides_points(sK2_skl,sK3_skl,sK1_skl)
& divides_points(sK2_skl,sK3_skl,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(B,sK0_skl),skolemize(C,sK1_skl),skolemize(L,sK2_skl),skolemize(A,sK3_skl)],[f131]) ).
fof(f133,plain,
divides_points(sK2_skl,sK3_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f143,plain,
( left_apart_point(sK0_skl,sK2_skl)
| left_apart_point(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f47,f133]) ).
fof(f144,definition,
( sQ0_spl
<=> left_apart_point(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ0_spl
| left_apart_point(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f151,definition,
( sQ2_spl
<=> left_apart_point(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ2_spl
| left_apart_point(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f155,plain,
( sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f143,f151,f144]) ).
fof(f180,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f145,f94]) ).
fof(f181,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f152,f94]) ).
fof(f187,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f180]) ).
fof(f188,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f189,plain,
$false,
inference(sat_refutation,[status(thm)],[f155,f187,f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO238+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 14:20:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.041969 seconds
% 0.10/0.42 % CPU time: 0.114074 seconds
% 0.10/0.42 % Total memory used: 16.571 MB
% 0.10/0.42 % Net memory used: 16.526 MB
%------------------------------------------------------------------------------