%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO204+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 : n020.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 12:24:29 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 10 unt; 10 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 64 ~; 79 |; 12 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 52 !; 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,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(f9,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,conjecture,
! [X,Y,Z] :
( ( ~ distinct_points(Y,Z)
& distinct_points(X,Y) )
=> ( ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ distinct_points(Y,Z)
& distinct_points(X,Y) )
=> ( ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
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(f35,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)],[f9]) ).
fof(f36,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)],[f35]) ).
fof(f45,plain,
? [X,Y,Z] :
( ( distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
| ~ distinct_points(X,Z) )
& ~ distinct_points(Y,Z)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( ( distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(sK0_skl,sK2_skl) )
& ~ distinct_points(sK1_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)],[f45]) ).
fof(f47,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
~ distinct_points(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
( distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,definition,
( sQ0_spl
<=> distinct_points(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( sQ0_spl
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,definition,
( sQ1_spl
<=> distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ1_spl
| distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f50,f53]) ).
fof(f57,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f20,f47]) ).
fof(f58,plain,
distinct_points(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f57,f48]) ).
fof(f59,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK1_skl,X1)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f57,f20]) ).
fof(f61,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f52]) ).
fof(f62,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f76,plain,
( distinct_points(sK1_skl,sK2_skl)
| distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f59,f48]) ).
fof(f86,definition,
( sQ4_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f93,definition,
( sQ6_spl
<=> distinct_points(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| distinct_points(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f76,f86,f93]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ1_spl
| apart_point_and_line(X1,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f36,f54]) ).
fof(f203,definition,
( sQ11_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( ~ sQ11_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f207,plain,
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f143,f47]) ).
fof(f236,definition,
( sQ12_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( ~ sQ12_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,definition,
( sQ13_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ13_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ14_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ14_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ15_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ15_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( ~ sQ1_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f207,f236,f239,f242,f245,f53]) ).
fof(f387,plain,
( ~ sQ13_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f240,f29]) ).
fof(f393,definition,
( sQ36_spl
<=> distinct_points(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( ~ sQ36_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,plain,
( ~ sQ13_spl
| sQ36_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f387,f50,f393,f239]) ).
fof(f398,plain,
( ~ sQ12_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f237,f29]) ).
fof(f404,plain,
( ~ sQ12_spl
| sQ36_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f398,f86,f393,f236]) ).
fof(f405,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f48]) ).
fof(f406,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f407,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f394,f15]) ).
fof(f408,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f407]) ).
fof(f534,plain,
( ~ sQ15_spl
| distinct_points(sK1_skl,sK2_skl)
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f246,f30]) ).
fof(f540,plain,
( ~ sQ15_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f534,f50,f93,f245]) ).
fof(f552,plain,
( ~ sQ14_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f243,f30]) ).
fof(f558,plain,
( ~ sQ14_spl
| sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f552,f86,f203,f242]) ).
fof(f560,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f15]) ).
fof(f561,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f562,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f62,f96,f248,f396,f404,f406,f408,f540,f558,f561]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:26:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.061896 seconds
% 0.14/0.43 % CPU time: 0.202495 seconds
% 0.14/0.43 % Total memory used: 17.960 MB
% 0.14/0.43 % Net memory used: 17.504 MB
%------------------------------------------------------------------------------