%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO191+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:24:23 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 10 unt; 7 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 178 ( 63 ~; 88 |; 13 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 78 ( 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,U,V] :
( ( ( apart_point_and_line(intersection_point(X,Y),V)
| apart_point_and_line(intersection_point(X,Y),U) )
& convergent_lines(U,V)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(U,V),Y)
| apart_point_and_line(intersection_point(U,V),X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ( apart_point_and_line(intersection_point(X,Y),V)
| apart_point_and_line(intersection_point(X,Y),U) )
& convergent_lines(U,V)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(U,V),Y)
| apart_point_and_line(intersection_point(U,V),X) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f19,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,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(f38,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)],[f37]) ).
fof(f39,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(f40,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,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)],[f40]) ).
fof(f45,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
? [X,Y,U,V] :
( ~ apart_point_and_line(intersection_point(U,V),Y)
& ~ apart_point_and_line(intersection_point(U,V),X)
& ( apart_point_and_line(intersection_point(X,Y),V)
| apart_point_and_line(intersection_point(X,Y),U) )
& convergent_lines(U,V)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( ~ apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK1_skl)
& ~ apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl)
& ( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) )
& convergent_lines(sK2_skl,sK3_skl)
& convergent_lines(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)],[f48]) ).
fof(f50,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
convergent_lines(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
~ apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
~ apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,definition,
( sQ0_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f58,definition,
( sQ1_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f55,f58]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( convergent_lines(X4,X3)
| ~ convergent_lines(X4,X2)
| 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_points(X0,X1) ),
inference(resolution,[status(thm)],[f38,f47]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( ~ convergent_lines(X3,X2)
| 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_points(X0,X1) ),
inference(resolution,[status(thm)],[f71,f19]) ).
fof(f76,plain,
! [X0,X1] :
( apart_point_and_line(X1,sK0_skl)
| apart_point_and_line(X1,sK1_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f74,f50]) ).
fof(f86,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl)
| ~ distinct_points(X0,intersection_point(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f76,f54]) ).
fof(f90,definition,
! [X0] :
( sQ2_spl
<=> ( apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl)
| ~ distinct_points(X0,intersection_point(sK2_skl,sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f91,plain,
! [X0] :
( ~ sQ2_spl
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl)
| ~ distinct_points(X0,intersection_point(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ3_spl
<=> apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f86,f90,f93]) ).
fof(f98,plain,
! [X0] :
( ~ sQ2_spl
| ~ convergent_lines(X0,sK1_skl)
| apart_point_and_line(intersection_point(X0,sK1_skl),sK0_skl)
| ~ distinct_points(intersection_point(X0,sK1_skl),intersection_point(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f91,f36]) ).
fof(f113,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f53]) ).
fof(f114,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f125,plain,
( ~ sQ2_spl
| ~ convergent_lines(sK0_skl,sK1_skl)
| ~ convergent_lines(sK0_skl,sK1_skl)
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f98,f34]) ).
fof(f127,definition,
( sQ6_spl
<=> distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( sQ6_spl
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
( sQ7_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( sQ7_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f125,f127,f130,f90]) ).
fof(f139,plain,
! [X0] :
( sQ6_spl
| apart_point_and_line(intersection_point(sK2_skl,sK3_skl),X0)
| ~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f129,f41]) ).
fof(f162,plain,
( sQ6_spl
| ~ convergent_lines(sK2_skl,sK3_skl)
| ~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f139,f36]) ).
fof(f163,plain,
( sQ6_spl
| ~ convergent_lines(sK2_skl,sK3_skl)
| ~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f139,f34]) ).
fof(f167,definition,
( sQ8_spl
<=> convergent_lines(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( sQ8_spl
| ~ convergent_lines(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( sQ6_spl
| ~ sQ8_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f162,f58,f167,f127]) ).
fof(f171,plain,
( sQ6_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f163,f55,f167,f127]) ).
fof(f172,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f51]) ).
fof(f173,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f50]) ).
fof(f175,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f176,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f96,f114,f133,f170,f171,f173,f175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO191+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 13:21:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.086061 seconds
% 0.14/0.46 % CPU time: 0.415645 seconds
% 0.14/0.46 % Total memory used: 20.589 MB
% 0.14/0.46 % Net memory used: 19.739 MB
%------------------------------------------------------------------------------