%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO237+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 : n018.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% 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 : 7 ( 6 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(f8,axiom,
! [A,B,L] :
( divides_points(L,A,B)
<=> ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,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(f38,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)],[f37]) ).
fof(f69,plain,
! [A,B,L] :
( ( ( ( ~ left_apart_point(B,L)
| ~ right_apart_point(A,L) )
& ( ~ right_apart_point(B,L)
| ~ left_apart_point(A,L) ) )
| divides_points(L,A,B) )
& ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f70,plain,
( ! [A,B,L] :
( ( ( ~ left_apart_point(B,L)
| ~ right_apart_point(A,L) )
& ( ~ right_apart_point(B,L)
| ~ left_apart_point(A,L) ) )
| divides_points(L,A,B) )
& ! [A,B,L] :
( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f72,plain,
! [X0,X1,X2] :
( left_apart_point(X2,X0)
| left_apart_point(X1,X0)
| ~ divides_points(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f113,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f114,plain,
( ! [A,L] : ~ left_apart_point(A,reverse_line(L))
& ! [A,L] : ~ left_apart_point(A,L) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f115,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f152,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)],[f38]) ).
fof(f153,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)],[f152]) ).
fof(f154,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)],[f153]) ).
fof(f156,plain,
divides_points(sK1_skl,sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f175,definition,
( sQ2_spl
<=> left_apart_point(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ2_spl
| left_apart_point(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f182,plain,
( left_apart_point(sK3_skl,sK1_skl)
| left_apart_point(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f72,f156]) ).
fof(f183,definition,
( sQ4_spl
<=> left_apart_point(sK3_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ4_spl
| left_apart_point(sK3_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f182,f175,f183]) ).
fof(f195,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f176,f115]) ).
fof(f198,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f200,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f115]) ).
fof(f201,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f202,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f198,f201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO237+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.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 14:17:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.040474 seconds
% 0.13/0.41 % CPU time: 0.105288 seconds
% 0.13/0.41 % Total memory used: 15.026 MB
% 0.13/0.41 % Net memory used: 14.980 MB
%------------------------------------------------------------------------------