%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO209+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 : n011.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 12:24:31 PM UTC 2026
% Result : Theorem 0.09s 15.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 24 ~; 21 |; 27 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 56 ( 48 !; 8 ?)
% 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(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,
! [A,L,M,N] :
( ( parallel_lines(N,L)
& parallel_lines(M,L)
& incident_point_and_line(A,N)
& incident_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> equal_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A,L,M,N] :
( ( parallel_lines(N,L)
& parallel_lines(M,L)
& incident_point_and_line(A,N)
& incident_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> equal_lines(M,N) ),
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(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,
? [A,L,M,N] :
( ~ equal_lines(M,N)
& parallel_lines(N,L)
& parallel_lines(M,L)
& incident_point_and_line(A,N)
& incident_point_and_line(A,M)
& apart_point_and_line(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
? [M,N] :
( ~ equal_lines(M,N)
& ? [L] :
( parallel_lines(N,L)
& parallel_lines(M,L)
& ? [A] :
( incident_point_and_line(A,N)
& incident_point_and_line(A,M)
& apart_point_and_line(A,L) ) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ~ equal_lines(sK0_skl,sK1_skl)
& parallel_lines(sK1_skl,sK2_skl)
& parallel_lines(sK0_skl,sK2_skl)
& incident_point_and_line(sK3_skl,sK1_skl)
& incident_point_and_line(sK3_skl,sK0_skl)
& apart_point_and_line(sK3_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(L,sK2_skl),skolemize(A,sK3_skl)],[f128]) ).
fof(f133,plain,
parallel_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f134,plain,
parallel_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f135,plain,
~ equal_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f146,plain,
distinct_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f114,f135]) ).
fof(f149,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f70,f146]) ).
fof(f151,plain,
! [X0] :
( convergent_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f149,f49]) ).
fof(f159,plain,
! [X0] :
( ~ parallel_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f151,f117]) ).
fof(f164,plain,
convergent_lines(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f159,f134]) ).
fof(f167,plain,
~ parallel_lines(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f164,f117]) ).
fof(f168,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f167,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.43 % CPULimit : 300
% 0.09/15.43 % WCLimit : 300
% 0.09/15.43 % DateTime : Sun Sep 20 13:29:22 UTC 2026
% 0.09/15.44 % CPUTime :
% 0.09/15.45 % Drodi V4.1.1
% 0.09/15.47 % Refutation found
% 0.09/15.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/15.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.35/15.50 % Elapsed time: 0.047836 seconds
% 0.35/15.50 % CPU time: 0.123172 seconds
% 0.35/15.50 % Total memory used: 18.206 MB
% 0.35/15.50 % Net memory used: 18.132 MB
%------------------------------------------------------------------------------