%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO182+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:24:20 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 80 ( 11 unt; 11 def)
% Number of atoms : 212 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 194 ( 62 ~; 102 |; 10 &)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 91 ( 85 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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(f13,conjecture,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(Z,line_connecting(Y,X)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(Z,line_connecting(Y,X)) ) ),
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(f40,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)],[f11]) ).
fof(f41,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f45,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(Y,X))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
? [X,Y] :
( ? [Z] :
( ~ apart_point_and_line(Z,line_connecting(Y,X))
& apart_point_and_line(Z,line_connecting(X,Y)) )
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ apart_point_and_line(sK2_skl,line_connecting(sK1_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)],[f46]) ).
fof(f48,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
~ apart_point_and_line(sK2_skl,line_connecting(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f20,f48]) ).
fof(f52,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK1_skl,X1)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f51,f20]) ).
fof(f62,plain,
! [X0] :
( distinct_points(X0,sK1_skl)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f52,f15]) ).
fof(f65,definition,
( sQ0_spl
<=> distinct_points(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f72,definition,
( sQ2_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( sQ2_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
! [X0,X1] :
( sQ3_spl
<=> ( distinct_points(X1,X0)
| distinct_points(sK1_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f76,plain,
! [X0,X1] :
( ~ sQ3_spl
| distinct_points(X1,X0)
| distinct_points(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f90,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f48]) ).
fof(f91,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f90]) ).
fof(f94,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK0_skl,X1)
| distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f62,f20]) ).
fof(f154,plain,
! [X0] :
( distinct_points(X0,sK0_skl)
| distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f94,f15]) ).
fof(f157,definition,
! [X0,X1] :
( sQ12_spl
<=> ( distinct_points(X1,X0)
| distinct_points(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sQ12_spl
| distinct_points(X1,X0)
| distinct_points(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f161,plain,
! [X0,X1] :
( distinct_points(sK1_skl,X1)
| distinct_points(X0,X1)
| distinct_points(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f154,f20]) ).
fof(f250,plain,
( ~ sQ3_spl
| $false ),
inference(resolution,[status(thm)],[f76,f15]) ).
fof(f254,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f250]) ).
fof(f265,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f42,f49]) ).
fof(f281,plain,
! [X0,X1,X2] :
( 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)],[f265,f36]) ).
fof(f386,plain,
! [X0] :
( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f281,f48]) ).
fof(f417,definition,
! [X0] :
( sQ21_spl
<=> ( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK2_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f418,plain,
! [X0] :
( ~ sQ21_spl
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,definition,
( sQ22_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( ~ sQ22_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,definition,
( sQ23_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( ~ sQ23_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f386,f417,f420,f423]) ).
fof(f517,plain,
( ~ sQ23_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f424,f30]) ).
fof(f521,definition,
( sQ42_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( ~ sQ42_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( ~ sQ23_spl
| sQ42_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f517,f72,f521,f423]) ).
fof(f526,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f15]) ).
fof(f527,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f552,plain,
( ~ sQ22_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f421,f29]) ).
fof(f556,definition,
( sQ45_spl
<=> distinct_points(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( ~ sQ45_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f559,plain,
( ~ sQ22_spl
| sQ45_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f552,f72,f556,f420]) ).
fof(f560,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f15]) ).
fof(f561,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f660,plain,
( ~ sQ12_spl
| $false ),
inference(resolution,[status(thm)],[f158,f15]) ).
fof(f670,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f687,plain,
! [X0,X1] :
( distinct_points(X1,X0)
| distinct_points(sK1_skl,X0)
| distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f161,f20]) ).
fof(f703,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f687,f65,f75]) ).
fof(f1214,plain,
( ~ sQ21_spl
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f418,f50]) ).
fof(f1219,definition,
( sQ89_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1220,plain,
( ~ sQ89_spl
| apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f1219]) ).
fof(f1222,definition,
( sQ90_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1223,plain,
( ~ sQ90_spl
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f1222]) ).
fof(f1225,plain,
( ~ sQ21_spl
| sQ90_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f1214,f1219,f1222,f417]) ).
fof(f1260,plain,
( ~ sQ89_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f1220,f30]) ).
fof(f1264,plain,
( ~ sQ89_spl
| sQ45_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1260,f65,f556,f1219]) ).
fof(f1267,plain,
( ~ sQ90_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f1223,f29]) ).
fof(f1271,plain,
( ~ sQ90_spl
| sQ42_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1267,f65,f521,f1222]) ).
fof(f1272,plain,
$false,
inference(sat_refutation,[status(thm)],[f91,f254,f426,f524,f527,f559,f561,f670,f703,f1225,f1264,f1271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO182+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 13:06:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.47 % Elapsed time: 0.103745 seconds
% 0.14/0.47 % CPU time: 0.578937 seconds
% 0.14/0.47 % Total memory used: 22.376 MB
% 0.14/0.47 % Net memory used: 21.215 MB
%------------------------------------------------------------------------------