%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO218+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 01:17:34 PM UTC 2026
% Result : Theorem 3.48s 1.06s
% Output : Proof 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 81 ( 36 ~; 29 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 51 ( 0 sgn 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [L,M,N] :
( ( ( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N) )
& ( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ) )
=> ( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cotno1) ).
fof(f13_nnf,plain,
! [L,M,N] :
( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N)
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ( unorthogonal_lines(L,M)
& convergent_lines(L,M) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [L,M,N] :
( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N)
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ( unorthogonal_lines(L,M)
& convergent_lines(L,M) ) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c16,plain,
( ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f5,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).
fof(f5_nnf,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f12,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
fof(f12_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c14,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f15,conjecture,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ convergent_lines(L,M) )
=> ~ unorthogonal_lines(M,N) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f15_neg,negated_conjecture,
~ ! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ convergent_lines(L,M) )
=> ~ unorthogonal_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f15_nnf,plain,
? [L,M,N] :
( unorthogonal_lines(M,N)
& ~ unorthogonal_lines(L,N)
& ~ convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15_neg]) ).
fof(f15_sk,plain,
( unorthogonal_lines(sk1,sk2)
& ~ unorthogonal_lines(sk0,sk2)
& ~ convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f15_nnf]) ).
cnf(c21,plain,
~ unorthogonal_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p23,plain,
convergent_lines(sk0,sk2),
inference(resolution,[status(thm)],[c14,c21]) ).
cnf(p31,plain,
( convergent_lines(sk2,X0)
| convergent_lines(sk0,X0) ),
inference(resolution,[status(thm)],[c5,p23]) ).
cnf(p34,plain,
( convergent_lines(X0,X1)
| convergent_lines(sk2,X1)
| convergent_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p31,c5]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f2_nnf,plain,
! [X] : ~ convergent_lines(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ convergent_lines(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p45,plain,
( convergent_lines(X0,sk2)
| convergent_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p34,c2]) ).
cnf(c20,plain,
~ convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p54,plain,
convergent_lines(sk1,sk2),
inference(resolution,[status(thm)],[p45,c20]) ).
cnf(p190,plain,
( ~ unorthogonal_lines(sk1,sk2)
| unorthogonal_lines(X0,sk2)
| convergent_lines(X0,sk1) ),
inference(resolution,[status(thm)],[c16,p54]) ).
cnf(c22,plain,
unorthogonal_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p553,plain,
( unorthogonal_lines(X0,sk2)
| convergent_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p190,c22]) ).
cnf(p585,plain,
convergent_lines(sk0,sk1),
inference(resolution,[status(thm)],[p553,c21]) ).
cnf(p586,plain,
$false,
inference(resolution,[status(thm)],[p585,c20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 % Computer : n015.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Wed Sep 23 11:35:39 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.48/1.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/1.06 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------