%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO196+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:24:26 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 15 unt; 2 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 33 |; 18 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
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(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y,U,V] :
( ( incident_point_and_line(intersection_point(X,Y),V)
& incident_point_and_line(intersection_point(X,Y),U)
& convergent_lines(U,V)
& convergent_lines(X,Y) )
=> ( incident_point_and_line(intersection_point(U,V),Y)
& incident_point_and_line(intersection_point(U,V),X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(intersection_point(X,Y),V)
& incident_point_and_line(intersection_point(X,Y),U)
& convergent_lines(U,V)
& convergent_lines(X,Y) )
=> ( incident_point_and_line(intersection_point(U,V),Y)
& incident_point_and_line(intersection_point(U,V),X) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(intersection_point(U,V),Y)
| ~ incident_point_and_line(intersection_point(U,V),X) )
& incident_point_and_line(intersection_point(X,Y),V)
& incident_point_and_line(intersection_point(X,Y),U)
& convergent_lines(U,V)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ( ~ incident_point_and_line(intersection_point(sK2_skl,sK3_skl),sK1_skl)
| ~ incident_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) )
& incident_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl)
& incident_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)],[f127]) ).
fof(f133,plain,
( ~ incident_point_and_line(intersection_point(sK2_skl,sK3_skl),sK1_skl)
| ~ incident_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f144,definition,
( sQ0_spl
<=> incident_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ0_spl
| ~ incident_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ1_spl
<=> incident_point_and_line(intersection_point(sK2_skl,sK3_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ1_spl
| ~ incident_point_and_line(intersection_point(sK2_skl,sK3_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,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f49,f40]) ).
fof(f157,plain,
( sQ0_spl
| apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f122,f146]) ).
fof(f160,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[status(thm)],[f71,f152]) ).
fof(f167,plain,
! [X0,X1,X2] :
( convergent_lines(X0,parallel_through_point(X1,X2))
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f160,f49]) ).
fof(f213,plain,
! [X0,X1,X2] : ~ convergent_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0),
inference(resolution,[status(thm)],[f167,f71]) ).
fof(f219,plain,
! [X0,X1,X2] : ~ convergent_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)),
inference(resolution,[status(thm)],[f213,f152]) ).
fof(f229,plain,
! [X0,X1,X2] : ~ distinct_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)),
inference(resolution,[status(thm)],[f219,f70]) ).
fof(f331,plain,
! [X0,X1,X2] :
( distinct_lines(X1,parallel_through_point(X2,X0))
| ~ apart_point_and_line(X0,X1) ),
inference(resolution,[status(thm)],[f65,f72]) ).
fof(f343,plain,
! [X0,X1] : ~ apart_point_and_line(X0,X1),
inference(resolution,[status(thm)],[f331,f229]) ).
fof(f348,plain,
! [X0,X1] : incident_point_and_line(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f122,f343]) ).
fof(f349,plain,
( sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f157,f343]) ).
fof(f350,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f387,plain,
( sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f149,f348]) ).
fof(f388,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f389,plain,
$false,
inference(sat_refutation,[status(thm)],[f150,f350,f388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO196+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:18:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.46 % Refutation found
% 0.12/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.114682 seconds
% 0.12/0.47 % CPU time: 0.649203 seconds
% 0.12/0.47 % Total memory used: 24.550 MB
% 0.12/0.47 % Net memory used: 23.287 MB
%------------------------------------------------------------------------------