%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO262+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 01:17:46 PM UTC 2026
% Result : Theorem 9.03s 1.67s
% Output : Proof 9.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 93 ( 29 ~; 27 |; 32 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 2 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,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',ax9_basics) ).
fof(f18_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)],[f18]) ).
fof(f18_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)],[f18_nnf]) ).
cnf(c44,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)],[f18_sk]) ).
fof(f6,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a7_defns) ).
fof(f6_nnf,plain,
! [L,M] :
( ( ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [L,M] :
( ( ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c13,plain,
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f36,conjecture,
! [L,M,N,A,B,C] :
( ( incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& incident_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(f36_neg,negated_conjecture,
~ ! [L,M,N,A,B,C] :
( ( incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& incident_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)],[f36]) ).
fof(f36_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)))
& incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& incident_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ~ between_on_line(sk1,intersection_point(sk1,parallel_through_point(sk2,sk3)),sk4,intersection_point(sk1,parallel_through_point(sk2,sk5)))
& incident_point_and_line(sk4,sk2)
& convergent_lines(sk1,sk2)
& convergent_lines(sk0,sk2)
& incident_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])],[f36_nnf]) ).
cnf(c67,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p75,plain,
unequally_directed_lines(sk0,sk1),
inference(resolution,[status(thm)],[c13,c67]) ).
cnf(p279,plain,
( left_convergent_lines(sk0,reverse_line(sk1))
| left_convergent_lines(sk0,sk1)
| ~ unequally_directed_lines(sk0,reverse_line(sk1)) ),
inference(resolution,[status(thm)],[c44,p75]) ).
cnf(c14,plain,
( unequally_directed_opposite_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p78,plain,
unequally_directed_opposite_lines(sk0,sk1),
inference(resolution,[status(thm)],[c14,c67]) ).
fof(f0,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1_defns) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p81,plain,
unequally_directed_lines(sk0,reverse_line(sk1)),
inference(resolution,[status(thm)],[p78,c0]) ).
cnf(p4815,plain,
( left_convergent_lines(sk0,reverse_line(sk1))
| left_convergent_lines(sk0,sk1) ),
inference(resolution,[status(thm)],[p279,p81]) ).
fof(f20,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11_basics) ).
fof(f20_nnf,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c47,plain,
~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p4816,plain,
left_convergent_lines(sk0,sk1),
inference(resolution,[status(thm)],[p4815,c47]) ).
cnf(p4817,plain,
$false,
inference(resolution,[status(thm)],[p4816,c47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO262+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.42 % Computer : n009.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Wed Sep 23 11:44:59 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.03/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.03/1.67 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------