%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO178+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:24:18 PM UTC 2026
% Result : Theorem 0.17s 0.53s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 4 unt; 3 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 65 ( 27 ~; 22 |; 8 &)
% ( 3 <=>; 5 =>; 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 : 34 ( 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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(f16,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)],[f15]) ).
fof(f29,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f39,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f48,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)],[f16]) ).
fof(f49,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)],[f48]) ).
fof(f50,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
( ~ distinct_points(sK2_skl,sK1_skl)
| ~ distinct_points(sK2_skl,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,definition,
( sQ0_spl
<=> distinct_points(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f56,definition,
( sQ1_spl
<=> distinct_points(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56]) ).
fof(f63,plain,
! [X0] :
( apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| distinct_points(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f41,f51]) ).
fof(f68,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f63,f32]) ).
fof(f69,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| distinct_points(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f63,f30]) ).
fof(f71,definition,
( sQ2_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( sQ2_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( ~ sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f68,f56,f71]) ).
fof(f75,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f53,f71]) ).
fof(f76,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f50]) ).
fof(f77,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f74,f75,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO178+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.49 % Computer : n004.cluster.edu
% 0.17/0.49 % Model : x86_64 x86_64
% 0.17/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.49 % Memory : 8046.5625MB
% 0.17/0.49 % OS : Linux 6.8.0-71-generic
% 0.17/0.49 % CPULimit : 300
% 0.17/0.49 % WCLimit : 300
% 0.17/0.49 % DateTime : Sun Sep 20 13:00:05 UTC 2026
% 0.17/0.50 % CPUTime :
% 0.17/0.52 % Drodi V4.1.1
% 0.17/0.53 % Refutation found
% 0.17/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.60 % Elapsed time: 0.088883 seconds
% 0.23/0.60 % CPU time: 0.083895 seconds
% 0.23/0.60 % Total memory used: 2.245 MB
% 0.23/0.60 % Net memory used: 2.208 MB
%------------------------------------------------------------------------------