%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 76 ( 12 unt; 8 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 187 ( 74 ~; 83 |; 13 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 80 !; 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(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(f31,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y,Z] :
( ( equal_points(Y,Z)
& distinct_points(X,Y) )
=> ( equal_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,Z] :
( ( equal_points(Y,Z)
& distinct_points(X,Y) )
=> ( equal_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f41,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f50,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f51,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f58,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(f59,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)],[f58]) ).
fof(f60,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(f61,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,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)],[f61]) ).
fof(f107,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f108,plain,
( ! [X,Y] :
( distinct_points(X,Y)
| equal_points(X,Y) )
& ! [X,Y] :
( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f111,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f112,plain,
( ! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ! [X,Y] :
( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f127,plain,
? [X,Y,Z] :
( ( ~ equal_lines(line_connecting(X,Y),line_connecting(X,Z))
| ~ distinct_points(X,Z) )
& equal_points(Y,Z)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ( ~ equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(sK0_skl,sK2_skl) )
& equal_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)],[f127]) ).
fof(f129,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
equal_points(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
( ~ equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f142,definition,
( sQ0_spl
<=> distinct_points(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( sQ0_spl
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
( sQ1_spl
<=> equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ1_spl
| ~ equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f131,f142,f145]) ).
fof(f149,plain,
~ distinct_points(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f109,f130]) ).
fof(f152,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f43,f129]) ).
fof(f155,plain,
distinct_points(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f152,f149]) ).
fof(f158,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f144]) ).
fof(f159,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( sQ1_spl
| distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f147,f114]) ).
fof(f191,definition,
( sQ6_spl
<=> distinct_points(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ6_spl
| distinct_points(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f206,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)],[f59,f161]) ).
fof(f319,definition,
( sQ11_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( ~ sQ11_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f346,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)],[f206,f129]) ).
fof(f383,definition,
( sQ14_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( ~ sQ14_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,definition,
( sQ15_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f387,plain,
( ~ sQ15_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f403,definition,
( sQ19_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( ~ sQ19_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,definition,
( sQ20_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( ~ sQ20_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( sQ1_spl
| sQ20_spl
| sQ19_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f346,f383,f386,f403,f406,f145]) ).
fof(f522,plain,
( ~ sQ15_spl
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f387,f51]) ).
fof(f525,plain,
( ~ sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f522,f142,f386]) ).
fof(f526,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f149]) ).
fof(f527,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f528,plain,
( ~ sQ14_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f384,f51]) ).
fof(f531,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f129]) ).
fof(f532,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f533,plain,
( ~ sQ19_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f404,f53]) ).
fof(f536,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f129]) ).
fof(f537,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f541,plain,
! [X0] :
( ~ sQ20_spl
| apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))
| distinct_points(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f407,f62]) ).
fof(f752,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f38]) ).
fof(f753,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f752]) ).
fof(f1106,plain,
( ~ sQ20_spl
| ~ distinct_points(sK0_skl,sK2_skl)
| distinct_points(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f541,f53]) ).
fof(f1111,plain,
( ~ sQ20_spl
| ~ sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1106,f191,f142,f406]) ).
fof(f1113,plain,
$false,
inference(sat_refutation,[status(thm)],[f148,f159,f409,f525,f527,f532,f537,f753,f1111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 13:22:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.44 % Refutation found
% 0.09/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.46 % Elapsed time: 0.078547 seconds
% 0.09/0.46 % CPU time: 0.384442 seconds
% 0.09/0.46 % Total memory used: 21.621 MB
% 0.09/0.46 % Net memory used: 21.042 MB
%------------------------------------------------------------------------------