%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO255+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 : Fri Sep 25 01:17:44 PM UTC 2026
% Result : Theorem 42.03s 5.77s
% Output : Proof 42.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 20 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 153 ( 58 ~; 59 |; 29 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 79 ( 2 sgn 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [L,M] :
( ( line(M)
& line(L) )
=> ( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag8) ).
fof(f12_nnf,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M)
| ~ line(M)
| ~ line(L) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M)
| ~ line(M)
| ~ line(L) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c35,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f19,axiom,
! [L] :
( line(L)
=> line(reverse_line(L)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco4) ).
fof(f19_nnf,plain,
! [L] :
( line(reverse_line(L))
| ~ line(L) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [L] :
( line(reverse_line(L))
| ~ line(L) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c44,plain,
( line(reverse_line(X0))
| ~ line(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f31,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/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f31_neg,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)],[f31]) ).
fof(f31_nnf,plain,
? [L,A,B] :
( before_on_line(L,B,A)
& before_on_line(L,A,B)
& distinct_points(A,B)
& line(L) ),
inference(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
( before_on_line(sk0,sk2,sk1)
& before_on_line(sk0,sk1,sk2)
& distinct_points(sk1,sk2)
& line(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f31_nnf]) ).
cnf(c58,plain,
line(sk0),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p62,plain,
line(reverse_line(sk0)),
inference(resolution,[status(thm)],[c44,c58]) ).
cnf(p167,plain,
( unequally_directed_lines(reverse_line(sk0),reverse_line(X0))
| unequally_directed_lines(reverse_line(sk0),X0)
| ~ line(X0) ),
inference(resolution,[status(thm)],[c35,p62]) ).
cnf(p245,plain,
( unequally_directed_lines(reverse_line(sk0),reverse_line(sk0))
| unequally_directed_lines(reverse_line(sk0),sk0) ),
inference(resolution,[status(thm)],[p167,c58]) ).
fof(f9,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag5) ).
fof(f9_nnf,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c29,plain,
~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p256,plain,
unequally_directed_lines(reverse_line(sk0),sk0),
inference(resolution,[status(thm)],[p245,c29]) ).
fof(f10,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',oag6) ).
fof(f10_nnf,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c30,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p257,plain,
( unequally_directed_lines(sk0,X0)
| unequally_directed_lines(reverse_line(sk0),X0) ),
inference(resolution,[status(thm)],[p256,c30]) ).
cnf(p264,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(reverse_line(sk0),X1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p257,c30]) ).
fof(f3,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',bf_def) ).
fof(f3_nnf,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)],[f3]) ).
fof(f3_sk,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(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c17,plain,
( ~ unequally_directed_lines(X0,line_connecting(X1,X2))
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c60,plain,
before_on_line(sk0,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p77,plain,
~ unequally_directed_lines(sk0,line_connecting(sk1,sk2)),
inference(resolution,[status(thm)],[c17,c60]) ).
cnf(p282,plain,
( unequally_directed_lines(line_connecting(sk1,sk2),X0)
| unequally_directed_lines(reverse_line(sk0),X0) ),
inference(resolution,[status(thm)],[p264,p77]) ).
cnf(p343,plain,
unequally_directed_lines(reverse_line(sk0),line_connecting(sk1,sk2)),
inference(resolution,[status(thm)],[p282,c29]) ).
fof(f13,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',oag9) ).
fof(f13_nnf,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(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,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(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c36,plain,
( 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(esa)],[f13_sk]) ).
cnf(p355,plain,
( left_convergent_lines(reverse_line(sk0),reverse_line(line_connecting(sk1,sk2)))
| left_convergent_lines(reverse_line(sk0),line_connecting(sk1,sk2))
| ~ unequally_directed_lines(reverse_line(sk0),reverse_line(line_connecting(sk1,sk2))) ),
inference(resolution,[status(thm)],[p343,c36]) ).
cnf(c61,plain,
before_on_line(sk0,sk2,sk1),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p78,plain,
~ unequally_directed_lines(sk0,line_connecting(sk2,sk1)),
inference(resolution,[status(thm)],[c17,c61]) ).
cnf(p284,plain,
( unequally_directed_lines(line_connecting(sk2,sk1),X0)
| unequally_directed_lines(reverse_line(sk0),X0) ),
inference(resolution,[status(thm)],[p264,p78]) ).
fof(f24,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco9) ).
fof(f24_nnf,plain,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c51,plain,
~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p367,plain,
unequally_directed_lines(reverse_line(sk0),reverse_line(line_connecting(sk1,sk2))),
inference(resolution,[status(thm)],[p284,c51]) ).
cnf(p9864,plain,
( left_convergent_lines(reverse_line(sk0),reverse_line(line_connecting(sk1,sk2)))
| left_convergent_lines(reverse_line(sk0),line_connecting(sk1,sk2)) ),
inference(resolution,[status(thm)],[p355,p367]) ).
fof(f15,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag11) ).
fof(f15_nnf,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c39,plain,
~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p9886,plain,
left_convergent_lines(reverse_line(sk0),line_connecting(sk1,sk2)),
inference(resolution,[status(thm)],[p9864,c39]) ).
cnf(p9887,plain,
$false,
inference(resolution,[status(thm)],[p9886,c39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO255+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n006.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 : Wed Sep 23 11:42:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 42.03/5.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.03/5.77 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------