%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO173+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 12:24:16 PM UTC 2026
% Result : Theorem 0.24s 5.50s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 12 unt; 7 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 47 ~; 53 |; 20 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 47 ( 39 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
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] :
( ( distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,U,V] :
( ( distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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] :
( ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
? [X,Y,U] :
( ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& distinct_lines(U,line_connecting(X,Y))
& ? [V] : convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ apart_point_and_line(sK1_skl,sK2_skl)
& ~ apart_point_and_line(sK0_skl,sK2_skl)
& distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_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,
distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
~ apart_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
~ apart_point_and_line(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f63,plain,
! [X0,X1] :
( apart_point_and_line(sK1_skl,X1)
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X1)
| apart_point_and_line(sK0_skl,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f36,f48]) ).
fof(f68,plain,
( apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK1_skl,sK2_skl)
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f63,f50]) ).
fof(f74,definition,
( sQ0_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ1_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ1_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ2_spl
<=> apart_point_and_line(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ2_spl
| apart_point_and_line(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ3_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ3_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f74,f77,f80,f83]) ).
fof(f139,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f52]) ).
fof(f140,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f51]) ).
fof(f142,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f141]) ).
fof(f174,plain,
( ~ sQ1_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f78,f29]) ).
fof(f179,definition,
( sQ12_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ12_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f183,definition,
( sQ13_spl
<=> distinct_points(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ13_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( ~ sQ1_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f174,f179,f183,f77]) ).
fof(f187,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f15]) ).
fof(f188,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f189,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f48]) ).
fof(f190,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f191,plain,
( ~ sQ3_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f84,f30]) ).
fof(f197,definition,
( sQ14_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ14_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( ~ sQ3_spl
| sQ14_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f191,f179,f197,f83]) ).
fof(f205,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f15]) ).
fof(f206,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f207,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f140,f142,f186,f188,f190,f200,f206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO173+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n026.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Sun Sep 20 12:57:41 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.48 % Drodi V4.1.1
% 0.24/5.50 % Refutation found
% 0.24/5.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/5.55 % Elapsed time: 0.077261 seconds
% 0.24/5.55 % CPU time: 0.118447 seconds
% 0.24/5.55 % Total memory used: 3.614 MB
% 0.24/5.55 % Net memory used: 3.570 MB
%------------------------------------------------------------------------------