%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO187+1 : TPTP v9.3.1. Released v3.3.0.
% 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 12:24:22 PM UTC 2026
% Result : Theorem 0.14s 0.48s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 9 unt; 6 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 193 ( 70 ~; 94 |; 17 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 62 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,U,V] :
( ( ~ apart_point_and_line(Y,line_connecting(U,V))
& ~ apart_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( ~ apart_point_and_line(V,line_connecting(X,Y))
& ~ apart_point_and_line(U,line_connecting(X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ~ apart_point_and_line(Y,line_connecting(U,V))
& ~ apart_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( ~ apart_point_and_line(V,line_connecting(X,Y))
& ~ apart_point_and_line(U,line_connecting(X,Y)) ) ),
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(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,U,V] :
( ( apart_point_and_line(V,line_connecting(X,Y))
| apart_point_and_line(U,line_connecting(X,Y)) )
& ~ apart_point_and_line(Y,line_connecting(U,V))
& ~ apart_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( ( apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) )
& ~ apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))
& ~ apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))
& distinct_points(sK2_skl,sK3_skl)
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f48]) ).
fof(f50,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
distinct_points(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
~ apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
~ apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
( apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,definition,
( sQ0_spl
<=> apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ0_spl
| apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,definition,
( sQ1_spl
<=> apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ1_spl
| apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f55,f58]) ).
fof(f63,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f56,f44]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| apart_point_and_line(X2,X0)
| apart_point_and_line(X2,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X1,X0)
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X1,X2)
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f63,f38]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ distinct_points(sK2_skl,X2)
| apart_point_and_line(X1,line_connecting(sK2_skl,X2))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK2_skl,X2))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f67,f30]) ).
fof(f91,plain,
! [X0] :
( ~ sQ1_spl
| apart_point_and_line(sK3_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f59,f44]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| apart_point_and_line(X2,X0)
| apart_point_and_line(X2,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X1,X0)
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X1,X2)
| apart_point_and_line(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f91,f38]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ distinct_points(X2,sK3_skl)
| apart_point_and_line(X1,line_connecting(X2,sK3_skl))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(X2,sK3_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f99,f32]) ).
fof(f112,plain,
! [X0,X1] :
( ~ sQ1_spl
| apart_point_and_line(X1,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f101,f51]) ).
fof(f157,plain,
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f112,f50]) ).
fof(f174,definition,
( sQ11_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ11_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,definition,
( sQ12_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ12_spl
| apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
( sQ13_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ13_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,definition,
( sQ14_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ14_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( ~ sQ1_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f157,f174,f177,f180,f183,f58]) ).
fof(f187,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f53]) ).
fof(f188,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f189,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f52]) ).
fof(f190,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f191,plain,
( ~ sQ13_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f181,f32]) ).
fof(f194,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f50]) ).
fof(f195,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f213,plain,
! [X0,X1] :
( ~ sQ0_spl
| apart_point_and_line(X1,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f70,f51]) ).
fof(f290,plain,
( ~ sQ0_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f213,f50]) ).
fof(f299,plain,
( ~ sQ0_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f290,f174,f177,f180,f183,f55]) ).
fof(f303,plain,
( ~ sQ11_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f175,f30]) ).
fof(f306,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f50]) ).
fof(f307,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f308,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f186,f188,f190,f195,f299,f307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 13:12:37 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.48 % Refutation found
% 0.14/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.51 % Elapsed time: 0.121865 seconds
% 0.14/0.51 % CPU time: 0.828227 seconds
% 0.14/0.51 % Total memory used: 26.767 MB
% 0.14/0.51 % Net memory used: 24.937 MB
%------------------------------------------------------------------------------