%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO262+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:24:46 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 9 unt; 1 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 171 ( 61 ~; 55 |; 48 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 106 ( 94 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [L,M,N] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [L,M,N,A,B,C] :
( ( ~ apart_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [L,M,N,A,B,C] :
( ( ~ apart_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f39,plain,
! [L,M] :
( ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
( ! [L,M] :
( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f78,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f79,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f80,plain,
! [L,M] :
( ! [N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) )
| ~ unequally_directed_lines(L,M) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [L,M,N] :
( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f83,definition,
! [L,N] :
( sP0_prd(N,L)
<=> ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f84,plain,
! [L,M,N] :
( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| sP0_prd(N,L)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(formula_renaming,[status(thm)],[f82,f83]) ).
fof(f85,plain,
! [L,M] :
( ! [N] :
( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| sP0_prd(N,L) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| sP0_prd(X2,X0)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f91,plain,
! [X0,X1] :
( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f96,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f97,plain,
( ! [L,M] : ~ left_convergent_lines(L,reverse_line(M))
& ! [L,M] : ~ left_convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f130,plain,
? [L,M,N,A,B,C] :
( ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C)))
& ~ apart_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
? [M,N,A,B,C] :
( ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C)))
& ~ apart_point_and_line(B,N)
& convergent_lines(M,N)
& ? [L] :
( convergent_lines(L,N)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
( ~ between_on_line(sK0_skl,intersection_point(sK0_skl,parallel_through_point(sK1_skl,sK2_skl)),sK3_skl,intersection_point(sK0_skl,parallel_through_point(sK1_skl,sK4_skl)))
& ~ apart_point_and_line(sK3_skl,sK1_skl)
& convergent_lines(sK0_skl,sK1_skl)
& convergent_lines(sK5_skl,sK1_skl)
& ~ apart_point_and_line(sK3_skl,sK0_skl)
& convergent_lines(sK5_skl,sK0_skl)
& between_on_line(sK5_skl,sK2_skl,sK3_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(L,sK5_skl)],[f131]) ).
fof(f137,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f140,plain,
! [L,N] :
( ( ~ unequally_directed_lines(L,reverse_line(N))
| ~ unequally_directed_lines(L,N)
| sP0_prd(N,L) )
& ( ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) )
| ~ sP0_prd(N,L) ) ),
inference(NNF_transformation,[status(thm)],[f83]) ).
fof(f141,plain,
( ! [L,N] :
( ~ unequally_directed_lines(L,reverse_line(N))
| ~ unequally_directed_lines(L,N)
| sP0_prd(N,L) )
& ! [L,N] :
( ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) )
| ~ sP0_prd(N,L) ) ),
inference(miniscoping,[status(thm)],[f140]) ).
fof(f143,plain,
! [X0,X1] :
( unequally_directed_lines(X1,reverse_line(X0))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f199,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X2)
| unequally_directed_lines(X2,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f81,f41]) ).
fof(f208,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| sP0_prd(X2,X0)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f86,f42]) ).
fof(f210,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unequally_directed_lines(X2,X0)
| sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f41]) ).
fof(f285,plain,
! [X0] :
( unequally_directed_lines(sK1_skl,X0)
| unequally_directed_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f199,f137]) ).
fof(f290,plain,
! [X0,X1] :
( left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f98]) ).
fof(f291,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f290,f98]) ).
fof(f297,plain,
unequally_directed_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f285,f78]) ).
fof(f315,plain,
! [X0] :
( unequally_directed_lines(sK1_skl,X0)
| sP0_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f210,f137]) ).
fof(f323,plain,
sP0_prd(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f315,f78]) ).
fof(f324,plain,
unequally_directed_lines(sK0_skl,reverse_line(sK1_skl)),
inference(resolution,[status(thm)],[f323,f143]) ).
fof(f362,plain,
~ unequally_directed_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f291,f324]) ).
fof(f367,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f362,f297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO262+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 14:51:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.47 % Elapsed time: 0.089055 seconds
% 0.11/0.47 % CPU time: 0.149198 seconds
% 0.11/0.47 % Total memory used: 5.250 MB
% 0.11/0.47 % Net memory used: 5.212 MB
%------------------------------------------------------------------------------