%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO230+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:24:38 PM UTC 2026
% Result : Theorem 0.24s 0.70s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 17 unt; 0 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 174 ( 69 ~; 90 |; 10 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 137 ( 135 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,L] : ~ unequally_directed_lines(parallel_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,L,M] :
( ( distinct_lines(L,M)
& distinct_points(A,B) )
=> ( left_apart_point(B,reverse_line(M))
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,reverse_line(L))
| left_apart_point(A,reverse_line(L))
| left_apart_point(B,M)
| left_apart_point(A,M)
| left_apart_point(B,L)
| left_apart_point(A,L) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B] :
( distinct_points(A,B)
=> ( ~ unequally_directed_lines(line_connecting(B,A),line_connecting(A,B))
& ~ distinct_lines(line_connecting(A,B),line_connecting(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
( distinct_points(A,B)
=> ( ~ unequally_directed_lines(line_connecting(B,A),line_connecting(A,B))
& ~ distinct_lines(line_connecting(A,B),line_connecting(B,A)) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
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(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(f92,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f93,plain,
( ! [A,L] : ~ left_apart_point(A,reverse_line(L))
& ! [A,L] : ~ left_apart_point(A,L) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[status(thm)],[f93]) ).
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(f116,plain,
! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f117,plain,
! [X0,X1] : ~ unequally_directed_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f118,plain,
! [A,B,L,M] :
( left_apart_point(B,reverse_line(M))
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,reverse_line(L))
| left_apart_point(A,reverse_line(L))
| left_apart_point(B,M)
| left_apart_point(A,M)
| left_apart_point(B,L)
| left_apart_point(A,L)
| ~ distinct_lines(L,M)
| ~ distinct_points(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f119,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X1,reverse_line(X3))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X0,reverse_line(X2))
| left_apart_point(X1,X3)
| left_apart_point(X0,X3)
| left_apart_point(X1,X2)
| left_apart_point(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f130,plain,
? [A,B] :
( ( unequally_directed_lines(line_connecting(B,A),line_connecting(A,B))
| distinct_lines(line_connecting(A,B),line_connecting(B,A)) )
& distinct_points(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
( ( unequally_directed_lines(line_connecting(sK1_skl,sK0_skl),line_connecting(sK0_skl,sK1_skl))
| distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl)) )
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f130]) ).
fof(f132,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
( unequally_directed_lines(line_connecting(sK1_skl,sK0_skl),line_connecting(sK0_skl,sK1_skl))
| distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f169,plain,
! [X0,X1] :
( unequally_directed_lines(X1,X0)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f81,f78]) ).
fof(f172,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X2,X0)
| ~ unequally_directed_lines(parallel_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f117,f81]) ).
fof(f179,plain,
! [X0,X1] : ~ unequally_directed_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[status(thm)],[f169,f117]) ).
fof(f195,plain,
! [X0,X1,X2] : ~ unequally_directed_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0),
inference(resolution,[status(thm)],[f172,f179]) ).
fof(f205,plain,
! [X0,X1,X2] : ~ unequally_directed_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)),
inference(resolution,[status(thm)],[f195,f169]) ).
fof(f214,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X2,reverse_line(line_connecting(X1,X0)))
| ~ unequally_directed_lines(line_connecting(X0,X1),X2) ),
inference(resolution,[status(thm)],[f116,f81]) ).
fof(f219,plain,
! [X0,X1,X2,X3] :
( unequally_directed_lines(X1,parallel_through_point(parallel_through_point(X0,X2),X3))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f205,f81]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X1,reverse_line(X3))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X0,reverse_line(X2))
| left_apart_point(X1,X3)
| left_apart_point(X0,X3)
| left_apart_point(X1,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f94]) ).
fof(f241,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X1,reverse_line(X3))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X1,X3)
| left_apart_point(X0,X3)
| left_apart_point(X1,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f240,f94]) ).
fof(f242,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X1,reverse_line(X3))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X1,X3)
| left_apart_point(X0,X3)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f241,f94]) ).
fof(f499,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X1,reverse_line(X3))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X1,X3)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f94]) ).
fof(f500,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X1,reverse_line(X3))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,X3)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f499,f94]) ).
fof(f501,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X1,reverse_line(X3))
| left_apart_point(X0,reverse_line(X3))
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f94]) ).
fof(f643,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X1,reverse_line(X3))
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f94]) ).
fof(f644,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f643,f94]) ).
fof(f645,plain,
! [X0,X1] : ~ distinct_lines(X0,X1),
inference(resolution,[status(thm)],[f644,f132]) ).
fof(f658,plain,
unequally_directed_lines(line_connecting(sK1_skl,sK0_skl),line_connecting(sK0_skl,sK1_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f133,f645]) ).
fof(f1095,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(f1096,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f1095,f98]) ).
fof(f1189,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(line_connecting(X2,X1),X0)
| ~ unequally_directed_lines(X0,line_connecting(X1,X2)) ),
inference(resolution,[status(thm)],[f1096,f214]) ).
fof(f1329,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(line_connecting(X1,X0),X2)
| ~ unequally_directed_lines(line_connecting(X0,X1),X2) ),
inference(resolution,[status(thm)],[f1189,f169]) ).
fof(f1992,plain,
! [X0,X1] : ~ unequally_directed_lines(X0,line_connecting(X1,X1)),
inference(resolution,[status(thm)],[f1329,f219]) ).
fof(f2051,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,line_connecting(X2,X2))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f1992,f81]) ).
fof(f2053,plain,
! [X0,X1] : ~ unequally_directed_lines(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f2051,f1992]) ).
fof(f2057,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f658,f2053]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO230+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.45 % Computer : n026.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Sun Sep 20 14:10:52 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.46 % Drodi V4.1.1
% 0.24/0.70 % Refutation found
% 0.24/0.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.75 % Elapsed time: 0.280850 seconds
% 0.24/0.75 % CPU time: 1.698512 seconds
% 0.24/0.75 % Total memory used: 32.031 MB
% 0.24/0.75 % Net memory used: 29.235 MB
%------------------------------------------------------------------------------