%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO175+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 : n017.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 12:24:17 PM UTC 2026
% Result : Theorem 0.14s 0.59s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 13 unt; 7 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 191 ( 73 ~; 81 |; 22 &)
% ( 7 <=>; 8 =>; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 71 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
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(f8,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
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(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y,U,V] :
( ( distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,U,V] :
( ( distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(X,V)
| 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(f31,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) ) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
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(f43,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
? [X,Y,U,V] :
( ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
? [X,U,V] :
( ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& ? [Y] : distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ apart_point_and_line(sK0_skl,sK2_skl)
& ~ apart_point_and_line(sK0_skl,sK1_skl)
& distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))
& convergent_lines(sK1_skl,sK2_skl)
& distinct_points(sK0_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(Y,sK3_skl)],[f46]) ).
fof(f48,plain,
distinct_points(sK0_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
~ apart_point_and_line(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
~ apart_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f65,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK1_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK2_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,f50]) ).
fof(f73,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),X0)
| apart_point_and_line(sK0_skl,X1)
| apart_point_and_line(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f65,f44]) ).
fof(f91,definition,
! [X1] :
( sQ3_spl
<=> ( apart_point_and_line(sK3_skl,X1)
| apart_point_and_line(sK0_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f92,plain,
! [X0] :
( ~ sQ3_spl
| apart_point_and_line(sK3_skl,X0)
| apart_point_and_line(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f102,definition,
( sQ4_spl
<=> apart_point_and_line(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ4_spl
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
( sQ5_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ5_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f125,plain,
! [X0,X1] :
( ~ sQ3_spl
| distinct_points(sK3_skl,X1)
| ~ distinct_points(X0,X1)
| apart_point_and_line(sK0_skl,line_connecting(X0,X1)) ),
inference(resolution,[status(thm)],[f92,f30]) ).
fof(f135,plain,
! [X0] :
( ~ sQ3_spl
| ~ distinct_points(X0,sK3_skl)
| apart_point_and_line(sK0_skl,line_connecting(X0,sK3_skl)) ),
inference(resolution,[status(thm)],[f125,f15]) ).
fof(f137,plain,
! [X0] :
( ~ sQ3_spl
| distinct_points(sK0_skl,X0)
| ~ distinct_points(X0,sK3_skl)
| ~ distinct_points(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f135,f29]) ).
fof(f144,definition,
( sQ10_spl
<=> distinct_points(sK0_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ10_spl
| ~ distinct_points(sK0_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f148,plain,
! [X0] :
( ~ sQ3_spl
| distinct_points(sK0_skl,X0)
| ~ distinct_points(X0,sK3_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f137]) ).
fof(f213,plain,
( apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl)
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl)
| apart_point_and_line(sK0_skl,sK2_skl)
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f73,f49]) ).
fof(f219,definition,
( sQ17_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ17_spl
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,definition,
( sQ18_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( ~ sQ18_spl
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( sQ18_spl
| sQ17_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f213,f102,f105,f219,f222]) ).
fof(f231,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f52]) ).
fof(f232,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f233,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f51]) ).
fof(f234,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f248,definition,
( sQ20_spl
<=> convergent_lines(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ20_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f252,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f49]) ).
fof(f253,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f252]) ).
fof(f674,plain,
! [X0] :
( ~ sQ17_spl
| distinct_points(intersection_point(sK1_skl,sK2_skl),intersection_point(sK1_skl,X0))
| ~ convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f220,f33]) ).
fof(f676,plain,
( ~ sQ3_spl
| ~ distinct_points(sK0_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f148,f15]) ).
fof(f677,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f676,f48]) ).
fof(f678,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f677]) ).
fof(f694,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f48]) ).
fof(f695,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f694]) ).
fof(f727,plain,
( ~ sQ17_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f674,f15]) ).
fof(f728,plain,
( ~ sQ17_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f727,f248,f219]) ).
fof(f731,plain,
! [X0] :
( ~ sQ18_spl
| distinct_points(intersection_point(sK1_skl,sK2_skl),intersection_point(X0,sK2_skl))
| ~ convergent_lines(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f223,f34]) ).
fof(f739,plain,
( ~ sQ18_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f731,f15]) ).
fof(f740,plain,
( ~ sQ18_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f739,f248,f222]) ).
fof(f741,plain,
$false,
inference(sat_refutation,[status(thm)],[f225,f232,f234,f253,f678,f695,f728,f740]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO175+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n017.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Sun Sep 20 12:56:42 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.55 % Drodi V4.1.1
% 0.14/0.59 % Refutation found
% 0.14/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.61 % Elapsed time: 0.061050 seconds
% 0.14/0.61 % CPU time: 0.323059 seconds
% 0.14/0.61 % Total memory used: 20.273 MB
% 0.14/0.61 % Net memory used: 19.474 MB
%------------------------------------------------------------------------------