%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO199+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 : n016.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 12:24:27 PM UTC 2026
% Result : Theorem 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 93 ( 17 unt; 9 def)
% Number of atoms : 286 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 296 ( 103 ~; 159 |; 17 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 111 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
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,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(Y,X),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(Y,X),Z) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
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,Z] :
( apart_point_and_line(intersection_point(Y,X),Z)
& ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK2_skl)
& ~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)
& convergent_lines(sK0_skl,sK2_skl)
& convergent_lines(sK2_skl,sK1_skl)
& convergent_lines(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)],[f45]) ).
fof(f47,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
convergent_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f52,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f34]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f33]) ).
fof(f58,plain,
! [X0,X1] :
( distinct_lines(X1,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f23,f16]) ).
fof(f62,plain,
! [X0,X1,X2,X3,X4] :
( ~ apart_point_and_line(X2,X4)
| ~ convergent_lines(X3,X4)
| apart_point_and_line(intersection_point(X3,X4),X1)
| apart_point_and_line(intersection_point(X3,X4),X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f36,f34]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X2,sK2_skl)
| apart_point_and_line(intersection_point(X2,sK2_skl),X1)
| apart_point_and_line(intersection_point(X2,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f62,f51]) ).
fof(f66,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f65,f49]) ).
fof(f70,plain,
! [X0,X1,X2] :
( distinct_lines(X2,X1)
| ~ distinct_lines(X2,X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f66,f23]) ).
fof(f73,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f66,f44]) ).
fof(f84,plain,
( apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f73,f47]) ).
fof(f89,definition,
( sQ3_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ3_spl
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,definition,
( sQ4_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( ~ sQ4_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
( sQ5_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ5_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f99,definition,
( sQ6_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ6_spl
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
( sQ7_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ7_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f106,plain,
( sQ5_spl
| sQ7_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f84,f99,f89,f102,f95]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ convergent_lines(X2,sK1_skl)
| apart_point_and_line(intersection_point(X2,sK1_skl),X1)
| apart_point_and_line(intersection_point(X2,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f96,f62]) ).
fof(f108,plain,
( ~ sQ7_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f103,f53]) ).
fof(f110,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f49]) ).
fof(f111,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f110]) ).
fof(f112,plain,
( ~ sQ3_spl
| ~ convergent_lines(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f90,f53]) ).
fof(f114,plain,
! [X0] :
( ~ sQ3_spl
| convergent_lines(X0,sK0_skl)
| ~ convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f112,f26]) ).
fof(f115,plain,
( ~ sQ6_spl
| ~ convergent_lines(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f100,f52]) ).
fof(f118,plain,
( ~ sQ3_spl
| convergent_lines(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f114,f47]) ).
fof(f120,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f17]) ).
fof(f121,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f122,plain,
! [X0] :
( ~ sQ6_spl
| convergent_lines(X0,sK0_skl)
| ~ convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f115,f26]) ).
fof(f124,plain,
( ~ sQ6_spl
| convergent_lines(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f122,f47]) ).
fof(f126,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f17]) ).
fof(f127,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f129,plain,
! [X0,X1] :
( ~ sQ5_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f107,f47]) ).
fof(f175,plain,
( ~ sQ4_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f93,f52]) ).
fof(f177,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f49]) ).
fof(f178,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f184,definition,
( sQ15_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ15_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f197,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X2)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X2)
| ~ distinct_lines(X2,X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f70,f129]) ).
fof(f201,definition,
! [X0,X2] :
( sQ18_spl
<=> ( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X2)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X2)
| ~ distinct_lines(X2,X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f202,plain,
! [X0,X1] :
( ~ sQ18_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| ~ distinct_lines(X1,X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
! [X1] :
( sQ19_spl
<=> ( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f205,plain,
! [X0] :
( ~ sQ19_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( ~ sQ5_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f197,f201,f204,f95]) ).
fof(f223,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ distinct_lines(X0,X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f202,f58]) ).
fof(f232,plain,
! [X0] :
( ~ sQ19_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f205]) ).
fof(f247,plain,
( ~ sQ19_spl
| ~ convergent_lines(sK0_skl,sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f232,f53]) ).
fof(f253,definition,
( sQ25_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ25_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ19_spl
| ~ sQ25_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f247,f99,f102,f253,f204]) ).
fof(f258,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f47]) ).
fof(f259,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f311,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f223,f44]) ).
fof(f322,plain,
( ~ sQ18_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f311,f49]) ).
fof(f326,plain,
( ~ sQ18_spl
| sQ15_spl
| sQ4_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f322,f99,f102,f92,f184,f201]) ).
fof(f328,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f50]) ).
fof(f329,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f330,plain,
$false,
inference(sat_refutation,[status(thm)],[f106,f111,f121,f127,f178,f207,f256,f259,f326,f329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO199+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n016.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sun Sep 20 13:23:13 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.13/5.41 % Refutation found
% 0.13/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.43 % Elapsed time: 0.053953 seconds
% 0.13/5.43 % CPU time: 0.178230 seconds
% 0.13/5.43 % Total memory used: 18.128 MB
% 0.13/5.43 % Net memory used: 17.712 MB
%------------------------------------------------------------------------------