%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO253+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 : n014.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 52 ( 24 ~; 11 |; 14 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,L] :
( apart_point_and_line(A,L)
<=> ( left_apart_point(A,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,L] :
( ( ~ apart_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) )
=> apart_point_and_line(B,L) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B,L] :
( ( ~ apart_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) )
=> apart_point_and_line(B,L) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
! [A,L] :
( ( ( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) )
| apart_point_and_line(A,L) )
& ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L)
| ~ apart_point_and_line(A,L) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f35,plain,
( ! [A,L] :
( ( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) )
| apart_point_and_line(A,L) )
& ! [A,L] :
( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L)
| ~ apart_point_and_line(A,L) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( left_apart_point(X0,reverse_line(X1))
| left_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
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,L] :
( ~ apart_point_and_line(B,L)
& ~ apart_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
? [B,L] :
( ~ apart_point_and_line(B,L)
& ? [A] :
( ~ apart_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
( ~ apart_point_and_line(sK0_skl,sK1_skl)
& ~ apart_point_and_line(sK0_skl,parallel_through_point(sK1_skl,sK2_skl))
& apart_point_and_line(sK2_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(B,sK0_skl),skolemize(L,sK1_skl),skolemize(A,sK2_skl)],[f131]) ).
fof(f133,plain,
apart_point_and_line(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f144,plain,
! [X0,X1] :
( left_apart_point(X0,reverse_line(X1))
| ~ apart_point_and_line(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f94]) ).
fof(f145,plain,
! [X0,X1] : ~ apart_point_and_line(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f144,f94]) ).
fof(f147,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f133,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO253+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n014.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 14:41:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.103922 seconds
% 0.15/0.46 % CPU time: 0.087865 seconds
% 0.15/0.46 % Total memory used: 4.191 MB
% 0.15/0.46 % Net memory used: 4.179 MB
%------------------------------------------------------------------------------