%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO188+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 : n003.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 12:24:22 PM UTC 2026
% Result : Theorem 0.07s 0.39s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 10 unt; 6 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 151 ( 55 ~; 68 |; 15 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 64 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f11,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,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(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ apart_point_and_line(X,line_connecting(Z,Y)) ),
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(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ apart_point_and_line(X,line_connecting(Z,Y)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
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(f37,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f42,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f48,plain,
? [X,Y,Z] :
( apart_point_and_line(X,line_connecting(Z,Y))
& ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl))
& ~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& distinct_points(sK1_skl,sK2_skl)
& distinct_points(sK0_skl,sK2_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(f52,plain,
distinct_points(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,plain,
! [X0] :
( distinct_points(sK2_skl,X0)
| distinct_points(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f22,f52]) ).
fof(f65,plain,
! [X0] :
( apart_point_and_line(sK0_skl,X0)
| distinct_lines(line_connecting(sK2_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f44,f54]) ).
fof(f75,definition,
( sQ1_spl
<=> distinct_points(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ1_spl
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f83,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,line_connecting(sK2_skl,sK1_skl))
| apart_point_and_line(X1,X0)
| apart_point_and_line(X1,line_connecting(sK2_skl,sK1_skl))
| ~ distinct_points(X1,X2)
| apart_point_and_line(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f65,f38]) ).
fof(f87,plain,
( sQ1_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f77,f55]) ).
fof(f88,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f17]) ).
fof(f89,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f334,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl))
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))
| apart_point_and_line(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f83,f52]) ).
fof(f372,definition,
( sQ16_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( ~ sQ16_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f379,definition,
( sQ18_spl
<=> apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( ~ sQ18_spl
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f420,definition,
! [X0] :
( sQ27_spl
<=> ( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f421,plain,
! [X0] :
( ~ sQ27_spl
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f446,plain,
( sQ18_spl
| sQ16_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f334,f420,f372,f379]) ).
fof(f535,plain,
( ~ sQ18_spl
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f380,f30]) ).
fof(f538,plain,
( ~ sQ18_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f535,f75,f379]) ).
fof(f540,plain,
( ~ sQ16_spl
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f373,f32]) ).
fof(f543,plain,
( ~ sQ16_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f540,f75,f372]) ).
fof(f745,plain,
( ~ sQ27_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f421,f53]) ).
fof(f751,definition,
( sQ61_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f752,plain,
( ~ sQ61_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f751]) ).
fof(f754,definition,
( sQ62_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f755,plain,
( ~ sQ62_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f757,plain,
( ~ sQ27_spl
| sQ62_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f745,f751,f754,f420]) ).
fof(f758,plain,
( ~ sQ61_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f752,f30]) ).
fof(f761,plain,
( ~ sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f758,f50]) ).
fof(f762,plain,
~ sQ61_spl,
inference(contradiction_clause,[status(thm)],[f761]) ).
fof(f763,plain,
( ~ sQ62_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f755,f32]) ).
fof(f766,plain,
( ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f763,f50]) ).
fof(f767,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f766]) ).
fof(f768,plain,
$false,
inference(sat_refutation,[status(thm)],[f89,f446,f538,f543,f757,f762,f767]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 13:10:44 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.39 % Refutation found
% 0.07/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.076600 seconds
% 0.15/0.43 % CPU time: 0.306009 seconds
% 0.15/0.43 % Total memory used: 18.983 MB
% 0.15/0.43 % Net memory used: 18.386 MB
%------------------------------------------------------------------------------