%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO196+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:24:25 PM UTC 2026
% Result : Theorem 0.13s 0.50s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 11 unt; 6 def)
% Number of atoms : 215 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 224 ( 83 ~; 110 |; 17 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 96 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ convergent_lines(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(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/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/sandbox/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(f17,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
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),sK2_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,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) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,definition,
( sQ0_spl
<=> apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ0_spl
| apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,definition,
( sQ1_spl
<=> apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ1_spl
| apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f55,f58]) ).
fof(f63,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,sK0_skl)
| distinct_points(intersection_point(sK2_skl,sK3_skl),X0) ),
inference(resolution,[status(thm)],[f41,f56]) ).
fof(f67,plain,
! [X0,X1] :
( ~ sQ0_spl
| distinct_points(X0,X1)
| distinct_points(intersection_point(sK2_skl,sK3_skl),X1)
| apart_point_and_line(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f63,f22]) ).
fof(f70,plain,
! [X0] :
( ~ sQ0_spl
| distinct_points(X0,intersection_point(sK2_skl,sK3_skl))
| apart_point_and_line(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f67,f17]) ).
fof(f74,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(f78,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)],[f74,f19]) ).
fof(f87,plain,
! [X0,X1] :
( apart_point_and_line(X1,sK2_skl)
| apart_point_and_line(X1,sK3_skl)
| apart_point_and_line(X0,sK2_skl)
| apart_point_and_line(X0,sK3_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f78,f51]) ).
fof(f92,plain,
! [X0,X1] :
( ~ convergent_lines(X1,sK3_skl)
| apart_point_and_line(intersection_point(X1,sK3_skl),sK2_skl)
| apart_point_and_line(X0,sK2_skl)
| apart_point_and_line(X0,sK3_skl)
| ~ distinct_points(X0,intersection_point(X1,sK3_skl)) ),
inference(resolution,[status(thm)],[f87,f36]) ).
fof(f98,definition,
( sQ3_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( ~ sQ3_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f113,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f52]) ).
fof(f114,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f124,plain,
! [X0] :
( ~ convergent_lines(sK2_skl,sK3_skl)
| ~ convergent_lines(sK2_skl,sK3_skl)
| apart_point_and_line(X0,sK2_skl)
| apart_point_and_line(X0,sK3_skl)
| ~ distinct_points(X0,intersection_point(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f92,f34]) ).
fof(f126,definition,
! [X0] :
( sQ5_spl
<=> ( apart_point_and_line(X0,sK2_skl)
| apart_point_and_line(X0,sK3_skl)
| ~ distinct_points(X0,intersection_point(sK2_skl,sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f127,plain,
! [X0] :
( ~ sQ5_spl
| apart_point_and_line(X0,sK2_skl)
| apart_point_and_line(X0,sK3_skl)
| ~ distinct_points(X0,intersection_point(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ6_spl
<=> convergent_lines(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ6_spl
| ~ convergent_lines(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f124,f126,f129]) ).
fof(f148,plain,
( ~ sQ5_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f127,f53]) ).
fof(f153,definition,
( sQ9_spl
<=> distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ9_spl
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( ~ sQ5_spl
| sQ3_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f148,f153,f98,f126]) ).
fof(f157,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f51]) ).
fof(f158,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( ~ sQ0_spl
| sQ9_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f155,f70]) ).
fof(f161,plain,
( ~ sQ0_spl
| sQ9_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f160,f34]) ).
fof(f164,plain,
( ~ sQ0_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f50]) ).
fof(f165,plain,
( ~ sQ0_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f167,plain,
! [X0] :
( ~ sQ1_spl
| apart_point_and_line(X0,sK1_skl)
| distinct_points(intersection_point(sK2_skl,sK3_skl),X0) ),
inference(resolution,[status(thm)],[f59,f41]) ).
fof(f168,plain,
! [X0,X1] :
( ~ sQ1_spl
| distinct_points(X0,X1)
| distinct_points(intersection_point(sK2_skl,sK3_skl),X1)
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f167,f22]) ).
fof(f171,plain,
! [X0] :
( ~ sQ1_spl
| distinct_points(X0,intersection_point(sK2_skl,sK3_skl))
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f168,f17]) ).
fof(f172,plain,
( sQ9_spl
| ~ sQ1_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f171,f155]) ).
fof(f198,plain,
( sQ9_spl
| ~ sQ1_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f172,f36]) ).
fof(f201,plain,
( sQ9_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f50]) ).
fof(f202,plain,
( sQ9_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f201]) ).
fof(f203,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f114,f132,f156,f158,f165,f202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO196+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.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 13:21:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.50 % Refutation found
% 0.13/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.52 % Elapsed time: 0.151221 seconds
% 0.13/0.52 % CPU time: 1.047374 seconds
% 0.13/0.52 % Total memory used: 25.818 MB
% 0.13/0.52 % Net memory used: 23.917 MB
%------------------------------------------------------------------------------