%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO238+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 : n012.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 0.02s 0.32s
% Output : CNFRefutation 0.02s
% 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 : 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(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] :
( ( divides_points(L,A,C)
& divides_points(L,A,B) )
=> ~ divides_points(L,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,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)],[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) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
? [B,C,L] :
( divides_points(L,B,C)
& ? [A] :
( divides_points(L,A,C)
& divides_points(L,A,B) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,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)],[f153]) ).
fof(f155,plain,
divides_points(sK2_skl,sK3_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f166,definition,
( sQ0_spl
<=> left_apart_point(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ0_spl
| left_apart_point(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f173,definition,
( sQ2_spl
<=> left_apart_point(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ2_spl
| left_apart_point(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f183,plain,
( left_apart_point(sK0_skl,sK2_skl)
| left_apart_point(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f72,f155]) ).
fof(f189,plain,
( sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f183,f173,f166]) ).
fof(f209,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f167,f115]) ).
fof(f210,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f174,f115]) ).
fof(f212,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f213,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f214,plain,
$false,
inference(sat_refutation,[status(thm)],[f189,f212,f213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO238+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 20 14:16:07 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.02/0.32 % Refutation found
% 0.02/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.33 % Elapsed time: 0.034671 seconds
% 0.07/0.33 % CPU time: 0.064819 seconds
% 0.07/0.33 % Total memory used: 19.206 MB
% 0.07/0.33 % Net memory used: 19.145 MB
%------------------------------------------------------------------------------