%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO253+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 : n004.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 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 6 unt; 2 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 29 ~; 21 |; 16 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 38 !; 6 ?)
% 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(f6,axiom,
! [A,L] :
( apart_point_and_line(A,L)
<=> ( right_apart_point(A,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,L] :
( ( incident_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(f38,negated_conjecture,
~ ! [A,B,L] :
( ( incident_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)],[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(f59,plain,
! [A,L] :
( ( ( ~ right_apart_point(A,L)
& ~ left_apart_point(A,L) )
| apart_point_and_line(A,L) )
& ( right_apart_point(A,L)
| left_apart_point(A,L)
| ~ apart_point_and_line(A,L) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f60,plain,
( ! [A,L] :
( ( ~ right_apart_point(A,L)
& ~ left_apart_point(A,L) )
| apart_point_and_line(A,L) )
& ! [A,L] :
( right_apart_point(A,L)
| left_apart_point(A,L)
| ~ apart_point_and_line(A,L) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( right_apart_point(X0,X1)
| left_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
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] :
( ~ apart_point_and_line(B,L)
& incident_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
? [B,L] :
( ~ apart_point_and_line(B,L)
& ? [A] :
( incident_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
( ~ apart_point_and_line(sK0_skl,sK1_skl)
& incident_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)],[f153]) ).
fof(f155,plain,
apart_point_and_line(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f163,plain,
( right_apart_point(sK2_skl,sK1_skl)
| left_apart_point(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f61,f155]) ).
fof(f164,definition,
( sQ0_spl
<=> left_apart_point(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ0_spl
| left_apart_point(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,definition,
( sQ1_spl
<=> right_apart_point(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ1_spl
| right_apart_point(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f163,f164,f167]) ).
fof(f173,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f165,f115]) ).
fof(f174,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f177,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f168,f178]) ).
fof(f178,plain,
! [X0,X1] : ~ right_apart_point(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f45,f115]) ).
fof(f179,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f180,plain,
$false,
inference(sat_refutation,[status(thm)],[f170,f174,f179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO253+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 14:38:34 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.049073 seconds
% 0.14/0.41 % CPU time: 0.113408 seconds
% 0.14/0.41 % Total memory used: 19.168 MB
% 0.14/0.41 % Net memory used: 19.095 MB
%------------------------------------------------------------------------------