%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO255+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 12:24:44 PM UTC 2026
% Result : Theorem 0.18s 0.56s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 167 ( 66 ~; 59 |; 34 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 84 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ ( left_apart_point(B,reverse_line(L))
| left_apart_point(B,L) )
& ~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) )
& distinct_points(A,B) ) ),
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(f13,axiom,
! [L,M] :
( ( line(M)
& line(L) )
=> ( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ) ),
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(f20,axiom,
! [L] :
( line(L)
=> line(reverse_line(L)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [L,A,B] :
( ( distinct_points(A,B)
& line(L) )
=> ~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [L,A,B] :
( ( distinct_points(A,B)
& line(L) )
=> ~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f52,plain,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ left_apart_point(B,reverse_line(L))
& ~ left_apart_point(B,L)
& ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L)
& distinct_points(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f53,plain,
! [L,A,B] :
( ( unequally_directed_lines(L,line_connecting(A,B))
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,L)
| left_apart_point(A,reverse_line(L))
| left_apart_point(A,L)
| ~ distinct_points(A,B)
| before_on_line(L,A,B) )
& ( ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ left_apart_point(B,reverse_line(L))
& ~ left_apart_point(B,L)
& ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
( ! [L,A,B] :
( unequally_directed_lines(L,line_connecting(A,B))
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,L)
| left_apart_point(A,reverse_line(L))
| left_apart_point(A,L)
| ~ distinct_points(A,B)
| before_on_line(L,A,B) )
& ! [L,A,B] :
( ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ left_apart_point(B,reverse_line(L))
& ~ left_apart_point(B,L)
& ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,line_connecting(X1,X2))
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
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(f88,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M)
| ~ line(M)
| ~ line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f89,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
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(f106,plain,
! [L] :
( line(reverse_line(L))
| ~ line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f107,plain,
! [X0] :
( line(reverse_line(X0))
| ~ line(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
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(f130,plain,
? [L,A,B] :
( before_on_line(L,B,A)
& before_on_line(L,A,B)
& distinct_points(A,B)
& line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
( before_on_line(sK0_skl,sK2_skl,sK1_skl)
& before_on_line(sK0_skl,sK1_skl,sK2_skl)
& distinct_points(sK1_skl,sK2_skl)
& line(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(L,sK0_skl),skolemize(A,sK1_skl),skolemize(B,sK2_skl)],[f130]) ).
fof(f132,plain,
line(sK0_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
before_on_line(sK0_skl,sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f135,plain,
before_on_line(sK0_skl,sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f145,plain,
! [X0] :
( unequally_directed_lines(X0,reverse_line(sK0_skl))
| unequally_directed_lines(X0,sK0_skl)
| ~ line(X0) ),
inference(resolution,[status(thm)],[f89,f132]) ).
fof(f146,plain,
! [X0] :
( ~ line(X0)
| unequally_directed_lines(reverse_line(X0),reverse_line(sK0_skl))
| unequally_directed_lines(reverse_line(X0),sK0_skl) ),
inference(resolution,[status(thm)],[f145,f107]) ).
fof(f180,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,reverse_line(line_connecting(X2,X1)))
| ~ unequally_directed_lines(X0,line_connecting(X1,X2)) ),
inference(resolution,[status(thm)],[f81,f116]) ).
fof(f182,plain,
! [X0,X1,X2,X3] :
( ~ before_on_line(X1,X2,X3)
| unequally_directed_lines(X0,line_connecting(X2,X3))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f81,f60]) ).
fof(f207,plain,
! [X0] :
( unequally_directed_lines(X0,line_connecting(sK2_skl,sK1_skl))
| ~ unequally_directed_lines(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f182,f135]) ).
fof(f208,plain,
! [X0] :
( unequally_directed_lines(X0,line_connecting(sK1_skl,sK2_skl))
| ~ unequally_directed_lines(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f182,f134]) ).
fof(f211,plain,
! [X0] :
( ~ line(X0)
| unequally_directed_lines(reverse_line(X0),reverse_line(sK0_skl))
| unequally_directed_lines(reverse_line(X0),line_connecting(sK2_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f207,f146]) ).
fof(f213,plain,
! [X0] :
( ~ line(X0)
| unequally_directed_lines(reverse_line(X0),reverse_line(sK0_skl))
| unequally_directed_lines(reverse_line(X0),line_connecting(sK1_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f208,f146]) ).
fof(f234,plain,
( ~ line(sK0_skl)
| unequally_directed_lines(reverse_line(sK0_skl),line_connecting(sK2_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f211,f78]) ).
fof(f235,plain,
unequally_directed_lines(reverse_line(sK0_skl),line_connecting(sK2_skl,sK1_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f234,f132]) ).
fof(f245,plain,
( ~ line(sK0_skl)
| unequally_directed_lines(reverse_line(sK0_skl),line_connecting(sK1_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f213,f78]) ).
fof(f246,plain,
unequally_directed_lines(reverse_line(sK0_skl),line_connecting(sK1_skl,sK2_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f245,f132]) ).
fof(f259,plain,
unequally_directed_lines(reverse_line(sK0_skl),reverse_line(line_connecting(sK2_skl,sK1_skl))),
inference(resolution,[status(thm)],[f246,f180]) ).
fof(f278,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(f279,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f278,f98]) ).
fof(f338,plain,
~ unequally_directed_lines(reverse_line(sK0_skl),line_connecting(sK2_skl,sK1_skl)),
inference(resolution,[status(thm)],[f279,f259]) ).
fof(f354,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f338,f235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO255+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n009.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 14:42:42 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 0.18/0.56 % Refutation found
% 0.18/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.60 % Elapsed time: 0.117503 seconds
% 0.18/0.60 % CPU time: 0.549878 seconds
% 0.18/0.60 % Total memory used: 17.842 MB
% 0.18/0.60 % Net memory used: 16.973 MB
%------------------------------------------------------------------------------