%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO178+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:24:18 PM UTC 2026
% Result : Theorem 0.03s 0.38s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 4 unt; 3 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 58 ( 22 ~; 18 |; 11 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f27,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X,Y] :
( ! [Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y)) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f45,plain,
? [X,Y,Z] :
( ( ~ distinct_points(Z,Y)
| ~ distinct_points(Z,X) )
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( ( ~ distinct_points(sK2_skl,sK1_skl)
| ~ distinct_points(sK2_skl,sK0_skl) )
& apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f45]) ).
fof(f47,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
( ~ distinct_points(sK2_skl,sK1_skl)
| ~ distinct_points(sK2_skl,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,definition,
( sQ0_spl
<=> distinct_points(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,definition,
( sQ1_spl
<=> distinct_points(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f50,f53]) ).
fof(f79,definition,
( sQ4_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( sQ4_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f91,plain,
( distinct_points(sK2_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f29,f48]) ).
fof(f92,plain,
( sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f91,f79,f50]) ).
fof(f93,plain,
( distinct_points(sK2_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f30,f48]) ).
fof(f94,plain,
( sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f93,f79,f53]) ).
fof(f95,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f47]) ).
fof(f96,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f95]) ).
fof(f97,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f92,f94,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO178+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.03/0.35 % CPULimit : 300
% 0.03/0.35 % WCLimit : 300
% 0.03/0.36 % DateTime : Sun Sep 20 12:55:56 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.37 % Drodi V4.1.1
% 0.03/0.38 % Refutation found
% 0.03/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.42 % Elapsed time: 0.041798 seconds
% 0.03/0.42 % CPU time: 0.113810 seconds
% 0.03/0.42 % Total memory used: 16.497 MB
% 0.03/0.42 % Net memory used: 16.088 MB
%------------------------------------------------------------------------------