%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO184+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 : n026.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 12:24:21 PM UTC 2026
% Result : Theorem 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 13 unt; 7 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 152 ( 56 ~; 61 |; 22 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 54 !; 8 ?)
% 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,U,V] :
( ( ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ~ distinct_lines(U,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ~ distinct_lines(U,line_connecting(X,Y)) ),
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,U,V] :
( distinct_lines(U,line_connecting(X,Y))
& ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
? [X,Y,U] :
( distinct_lines(U,line_connecting(X,Y))
& ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& ? [V] : convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& ~ apart_point_and_line(sK1_skl,sK2_skl)
& ~ apart_point_and_line(sK0_skl,sK2_skl)
& convergent_lines(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)],[f46]) ).
fof(f48,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
~ apart_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
~ apart_point_and_line(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f54,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f20,f48]) ).
fof(f57,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK1_skl,X1)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f54,f20]) ).
fof(f73,plain,
distinct_points(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f57,f15]) ).
fof(f88,definition,
( sQ2_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( sQ2_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f154,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X1,sK2_skl)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f36,f52]) ).
fof(f156,plain,
( apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,sK2_skl)
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f154,f73]) ).
fof(f167,definition,
( sQ10_spl
<=> apart_point_and_line(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ10_spl
| apart_point_and_line(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,definition,
( sQ11_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( ~ sQ11_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,definition,
( sQ12_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ12_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,definition,
( sQ13_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ13_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f156,f167,f170,f173,f176]) ).
fof(f208,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f50]) ).
fof(f209,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f217,plain,
( ~ sQ13_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f177,f29]) ).
fof(f222,definition,
( sQ20_spl
<=> distinct_points(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( ~ sQ20_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( ~ sQ13_spl
| sQ20_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f217,f88,f222,f176]) ).
fof(f226,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f48]) ).
fof(f227,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f15]) ).
fof(f229,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f230,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f51]) ).
fof(f231,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f232,plain,
( ~ sQ11_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f171,f30]) ).
fof(f237,definition,
( sQ21_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ21_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( ~ sQ11_spl
| sQ21_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f232,f88,f237,f170]) ).
fof(f242,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f15]) ).
fof(f243,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f242]) ).
fof(f244,plain,
$false,
inference(sat_refutation,[status(thm)],[f179,f209,f225,f227,f229,f231,f240,f243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO184+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n026.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 20 13:09:07 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.16/0.51 % Refutation found
% 0.16/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.53 % Elapsed time: 0.076634 seconds
% 0.16/0.53 % CPU time: 0.127094 seconds
% 0.16/0.53 % Total memory used: 5.319 MB
% 0.16/0.53 % Net memory used: 5.195 MB
%------------------------------------------------------------------------------