%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO237+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 : n019.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 0.40s
% 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 : 75 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 80 ( 30 ~; 22 |; 21 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 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] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,B,C)
| divides_points(L,A,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B,C,L] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,B,C)
| divides_points(L,A,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)
& apart_point_and_line(C,L) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
? [C,L] :
( ? [A,B] :
( ~ divides_points(L,B,C)
& ~ divides_points(L,A,C)
& divides_points(L,A,B) )
& apart_point_and_line(C,L) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
( ~ divides_points(sK1_skl,sK3_skl,sK0_skl)
& ~ divides_points(sK1_skl,sK2_skl,sK0_skl)
& divides_points(sK1_skl,sK2_skl,sK3_skl)
& apart_point_and_line(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(C,sK0_skl),skolemize(L,sK1_skl),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f131]) ).
fof(f134,plain,
divides_points(sK1_skl,sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f142,plain,
( left_apart_point(sK3_skl,sK1_skl)
| left_apart_point(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f47,f134]) ).
fof(f143,definition,
( sQ0_spl
<=> left_apart_point(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ0_spl
| left_apart_point(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ1_spl
<=> left_apart_point(sK3_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ1_spl
| left_apart_point(sK3_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f142,f143,f146]) ).
fof(f167,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f144,f94]) ).
fof(f172,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f173,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f94]) ).
fof(f174,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f175,plain,
$false,
inference(sat_refutation,[status(thm)],[f149,f172,f174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO237+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 14:15:04 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.039844 seconds
% 0.10/0.42 % CPU time: 0.104505 seconds
% 0.10/0.42 % Total memory used: 15.406 MB
% 0.10/0.42 % Net memory used: 15.365 MB
%------------------------------------------------------------------------------