%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO251+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 : n011.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 12:24:43 PM UTC 2026
% Result : Theorem 0.58s 15.72s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 30 ( 15 ~; 6 |; 6 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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 : 31 ( 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( right_apart_point(X,Y)
<=> left_apart_point(X,reverse_line(Y)) ),
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,L] :
( right_apart_point(B,parallel_through_point(L,A))
=> left_apart_point(A,parallel_through_point(L,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [A,B,L] :
( right_apart_point(B,parallel_through_point(L,A))
=> left_apart_point(A,parallel_through_point(L,B)) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f43,plain,
! [X,Y] :
( ( ~ left_apart_point(X,reverse_line(Y))
| right_apart_point(X,Y) )
& ( left_apart_point(X,reverse_line(Y))
| ~ right_apart_point(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f44,plain,
( ! [X,Y] :
( ~ left_apart_point(X,reverse_line(Y))
| right_apart_point(X,Y) )
& ! [X,Y] :
( left_apart_point(X,reverse_line(Y))
| ~ right_apart_point(X,Y) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( left_apart_point(X0,reverse_line(X1))
| ~ right_apart_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
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,L] :
( ~ left_apart_point(A,parallel_through_point(L,B))
& right_apart_point(B,parallel_through_point(L,A)) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
( ~ left_apart_point(sK0_skl,parallel_through_point(sK2_skl,sK1_skl))
& right_apart_point(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(L,sK2_skl)],[f152]) ).
fof(f154,plain,
right_apart_point(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f161,plain,
! [X0,X1] : ~ right_apart_point(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f45,f115]) ).
fof(f170,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f154,f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO251+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.15/15.69 % CPULimit : 300
% 0.15/15.69 % WCLimit : 300
% 0.15/15.69 % DateTime : Sun Sep 20 14:40:51 UTC 2026
% 0.15/15.70 % CPUTime :
% 0.58/15.71 % Drodi V4.1.1
% 0.58/15.72 % Refutation found
% 0.58/15.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.58/15.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.58/15.81 % Elapsed time: 0.103249 seconds
% 0.58/15.81 % CPU time: 0.073836 seconds
% 0.58/15.81 % Total memory used: 1.234 MB
% 0.58/15.81 % Net memory used: 1.230 MB
%------------------------------------------------------------------------------