%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO254+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 : n007.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 0.09s 0.56s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 11 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 207 ( 87 ~; 76 |; 37 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 114 ( 111 !; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : ~ distinct_points(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( distinct_points(A,B)
=> ( distinct_points(B,C)
| distinct_points(A,C) ) ),
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(f32,conjecture,
! [A,B,L] :
( ( ~ apart_point_and_line(B,L)
& ~ apart_point_and_line(A,L)
& distinct_points(A,B) )
=> ( before_on_line(L,B,A)
& before_on_line(L,A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B,L] :
( ( ~ apart_point_and_line(B,L)
& ~ apart_point_and_line(A,L)
& distinct_points(A,B) )
=> ( 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(f61,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,line_connecting(X1,X2))
| left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0)
| left_apart_point(X1,reverse_line(X0))
| left_apart_point(X1,X0)
| ~ distinct_points(X1,X2)
| before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f70,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f71,plain,
! [A,B,C] :
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
! [A,B] :
( ! [C] :
( distinct_points(B,C)
| distinct_points(A,C) )
| ~ distinct_points(A,B) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
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(f130,plain,
? [A,B,L] :
( ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,A,B) )
& ~ apart_point_and_line(B,L)
& ~ apart_point_and_line(A,L)
& distinct_points(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f131,plain,
( ( ~ before_on_line(sK2_skl,sK1_skl,sK0_skl)
| ~ before_on_line(sK2_skl,sK0_skl,sK1_skl) )
& ~ apart_point_and_line(sK1_skl,sK2_skl)
& ~ apart_point_and_line(sK0_skl,sK2_skl)
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(L,sK2_skl)],[f130]) ).
fof(f132,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f135,plain,
( ~ before_on_line(sK2_skl,sK1_skl,sK0_skl)
| ~ before_on_line(sK2_skl,sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f146,plain,
! [X0,X1] :
( distinct_points(X1,X0)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f73,f70]) ).
fof(f240,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,line_connecting(X1,X2))
| left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0)
| left_apart_point(X1,reverse_line(X0))
| ~ distinct_points(X1,X2)
| before_on_line(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f94]) ).
fof(f554,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(f555,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f554,f98]) ).
fof(f568,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X2,reverse_line(X1))
| ~ unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f555,f81]) ).
fof(f660,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,line_connecting(X2,X1))
| ~ unequally_directed_lines(X0,line_connecting(X1,X2)) ),
inference(resolution,[status(thm)],[f568,f116]) ).
fof(f912,plain,
! [X0,X1] : ~ unequally_directed_lines(X0,line_connecting(X1,X1)),
inference(factoring,[status(thm)],[f660]) ).
fof(f935,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,line_connecting(X2,X2))
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[f912,f81]) ).
fof(f937,plain,
! [X0,X1] : ~ unequally_directed_lines(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f935,f912]) ).
fof(f940,plain,
! [X0,X1,X2] :
( left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0)
| left_apart_point(X1,reverse_line(X0))
| ~ distinct_points(X1,X2)
| before_on_line(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f240,f937]) ).
fof(f943,plain,
! [X0,X1,X2] :
( left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0)
| ~ distinct_points(X1,X2)
| before_on_line(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f940,f94]) ).
fof(f945,plain,
! [X0,X1,X2] :
( left_apart_point(X2,reverse_line(X0))
| ~ distinct_points(X1,X2)
| before_on_line(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f943,f94]) ).
fof(f946,plain,
( ~ before_on_line(sK2_skl,sK0_skl,sK1_skl)
| left_apart_point(sK0_skl,reverse_line(sK2_skl))
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f945,f135]) ).
fof(f948,plain,
( ~ before_on_line(sK2_skl,sK0_skl,sK1_skl)
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f946,f94]) ).
fof(f949,plain,
( left_apart_point(sK1_skl,reverse_line(sK2_skl))
| ~ distinct_points(sK0_skl,sK1_skl)
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f948,f945]) ).
fof(f954,plain,
( left_apart_point(sK1_skl,reverse_line(sK2_skl))
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f949,f146]) ).
fof(f955,plain,
left_apart_point(sK1_skl,reverse_line(sK2_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f954,f132]) ).
fof(f956,plain,
$false,
inference(resolution,[status(thm)],[f955,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO254+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 14:42:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.56 % Refutation found
% 0.09/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.93/0.58 % Elapsed time: 0.195110 seconds
% 0.93/0.58 % CPU time: 1.358998 seconds
% 0.93/0.58 % Total memory used: 32.917 MB
% 0.93/0.58 % Net memory used: 29.473 MB
%------------------------------------------------------------------------------