%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO206+3 : TPTP v9.3.1. Bugfixed v4.0.1.
% 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 12:24:30 PM UTC 2026
% Result : Theorem 0.10s 5.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 24 ~; 20 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 49 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f32,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y,Z] :
( ( parallel_lines(Y,Z)
& incident_point_and_line(X,Y) )
=> equal_lines(Y,parallel_through_point(Z,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,Z] :
( ( parallel_lines(Y,Z)
& incident_point_and_line(X,Y) )
=> equal_lines(Y,parallel_through_point(Z,X)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
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(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(f111,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f112,plain,
( ! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ! [X,Y] :
( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f116,plain,
( ! [X,Y] :
( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f127,plain,
? [X,Y,Z] :
( ~ equal_lines(Y,parallel_through_point(Z,X))
& parallel_lines(Y,Z)
& incident_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ~ equal_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl))
& parallel_lines(sK1_skl,sK2_skl)
& incident_point_and_line(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)],[f127]) ).
fof(f130,plain,
parallel_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
~ equal_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f142,plain,
distinct_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)),
inference(resolution,[status(thm)],[f114,f131]) ).
fof(f149,plain,
convergent_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)),
inference(resolution,[status(thm)],[f142,f70]) ).
fof(f150,plain,
! [X0] :
( convergent_lines(parallel_through_point(sK2_skl,sK0_skl),X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f149,f49]) ).
fof(f156,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f150,f71]) ).
fof(f161,plain,
~ parallel_lines(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f156,f117]) ).
fof(f162,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f161,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO206+3 : TPTP v9.3.1. Bugfixed v4.0.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.35 % Computer : n002.cluster.edu
% 0.10/5.35 % Model : x86_64 x86_64
% 0.10/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.35 % Memory : 8046.5625MB
% 0.10/5.35 % OS : Linux 6.8.0-71-generic
% 0.10/5.35 % CPULimit : 300
% 0.10/5.35 % WCLimit : 300
% 0.10/5.35 % DateTime : Sun Sep 20 13:25:40 UTC 2026
% 0.10/5.35 % CPUTime :
% 0.10/5.36 % Drodi V4.1.1
% 0.10/5.38 % Refutation found
% 0.10/5.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.41 % Elapsed time: 0.045262 seconds
% 0.13/5.41 % CPU time: 0.122066 seconds
% 0.13/5.41 % Total memory used: 18.104 MB
% 0.13/5.41 % Net memory used: 18.035 MB
%------------------------------------------------------------------------------