%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:24:22 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 11 unt; 2 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 120 ( 35 ~; 58 |; 18 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 84 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : ~ distinct_lines(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(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y,U,V] :
( ( incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(V,line_connecting(X,Y))
& incident_point_and_line(U,line_connecting(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(V,line_connecting(X,Y))
& incident_point_and_line(U,line_connecting(X,Y)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f39,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f44,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f48,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f63,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f64,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f69,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f72,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f119,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f120,plain,
( ! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ! [X,Y] :
( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f122,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f127,plain,
? [X,Y,U,V] :
( ( ~ incident_point_and_line(V,line_connecting(X,Y))
| ~ incident_point_and_line(U,line_connecting(X,Y)) )
& incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ( ~ incident_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))
| ~ incident_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) )
& incident_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))
& incident_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))
& distinct_points(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)],[f127]) ).
fof(f133,plain,
( ~ incident_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))
| ~ incident_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f144,definition,
( sQ0_spl
<=> incident_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ0_spl
| ~ incident_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ1_spl
<=> incident_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ1_spl
| ~ incident_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f133,f144,f147]) ).
fof(f152,plain,
( sQ0_spl
| apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f122,f146]) ).
fof(f156,plain,
! [X0] :
( sQ0_spl
| apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f65,f152]) ).
fof(f158,plain,
! [X0,X1] :
( sQ0_spl
| distinct_lines(X0,X1)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X1)
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f156,f46]) ).
fof(f203,plain,
! [X0] :
( sQ0_spl
| distinct_lines(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f158,f39]) ).
fof(f207,plain,
! [X0] :
( sQ0_spl
| convergent_lines(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f203,f70]) ).
fof(f237,plain,
! [X0] :
( sQ0_spl
| apart_point_and_line(sK2_skl,parallel_through_point(line_connecting(sK0_skl,sK1_skl),X0)) ),
inference(resolution,[status(thm)],[f207,f71]) ).
fof(f248,plain,
( sQ0_spl
| $false ),
inference(resolution,[status(thm)],[f237,f72]) ).
fof(f252,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f253,plain,
( sQ1_spl
| apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f149,f122]) ).
fof(f254,plain,
! [X0] :
( sQ1_spl
| apart_point_and_line(sK3_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f253,f65]) ).
fof(f257,plain,
! [X0] :
( sQ1_spl
| convergent_lines(line_connecting(sK0_skl,sK1_skl),X0)
| apart_point_and_line(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f254,f70]) ).
fof(f275,plain,
! [X0,X1] :
( sQ1_spl
| convergent_lines(X0,X1)
| convergent_lines(line_connecting(sK0_skl,sK1_skl),X1)
| apart_point_and_line(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f257,f49]) ).
fof(f308,plain,
! [X0] :
( sQ1_spl
| convergent_lines(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f275,f40]) ).
fof(f347,plain,
! [X0] :
( sQ1_spl
| apart_point_and_line(sK3_skl,parallel_through_point(line_connecting(sK0_skl,sK1_skl),X0)) ),
inference(resolution,[status(thm)],[f308,f71]) ).
fof(f351,plain,
( sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f347,f72]) ).
fof(f355,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f356,plain,
$false,
inference(sat_refutation,[status(thm)],[f150,f252,f355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:08:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.062515 seconds
% 0.09/0.44 % CPU time: 0.222311 seconds
% 0.09/0.44 % Total memory used: 19.612 MB
% 0.09/0.44 % Net memory used: 19.321 MB
%------------------------------------------------------------------------------