%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO262+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 : n011.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 01:17:46 PM UTC 2026
% Result : Theorem 4.37s 21.07s
% Output : Proof 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 88 ( 32 ~; 22 |; 30 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,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/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f31_neg,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)],[f31]) ).
fof(f31_nnf,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(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
( ~ between_on_line(sk1,intersection_point(sk1,parallel_through_point(sk2,sk3)),sk4,intersection_point(sk1,parallel_through_point(sk2,sk5)))
& ~ apart_point_and_line(sk4,sk2)
& convergent_lines(sk1,sk2)
& convergent_lines(sk0,sk2)
& ~ apart_point_and_line(sk4,sk1)
& convergent_lines(sk0,sk1)
& between_on_line(sk0,sk3,sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5])],[f31_nnf]) ).
cnf(c59,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f1,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con_def) ).
fof(f1_nnf,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)],[f1]) ).
fof(f1_sk,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(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p79,plain,
unequally_directed_lines(sk0,sk1),
inference(resolution,[status(thm)],[c59,c3]) ).
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(p105,plain,
( left_convergent_lines(sk0,reverse_line(sk1))
| left_convergent_lines(sk0,sk1)
| ~ unequally_directed_lines(sk0,reverse_line(sk1)) ),
inference(resolution,[status(thm)],[p79,c36]) ).
cnf(c4,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p80,plain,
unequally_directed_lines(sk0,reverse_line(sk1)),
inference(resolution,[status(thm)],[c59,c4]) ).
cnf(p170,plain,
( left_convergent_lines(sk0,reverse_line(sk1))
| left_convergent_lines(sk0,sk1) ),
inference(resolution,[status(thm)],[p105,p80]) ).
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(p361,plain,
left_convergent_lines(sk0,sk1),
inference(resolution,[status(thm)],[p170,c39]) ).
cnf(p2308,plain,
$false,
inference(resolution,[status(thm)],[p361,c39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO262+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/20.43 % CPULimit : 300
% 0.07/20.43 % WCLimit : 300
% 0.07/20.43 % DateTime : Wed Sep 23 11:45:09 UTC 2026
% 0.07/20.43 % CPUTime :
% 0.07/20.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.37/21.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.37/21.07 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------