%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO213+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 : n003.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 01:17:32 PM UTC 2026
% Result : Theorem 4.70s 1.12s
% Output : Proof 4.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 24 ~; 36 |; 11 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 61 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
fof(f15_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c17,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f20,conjecture,
! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f20_neg,negated_conjecture,
~ ! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ distinct_lines(L,N)
& unorthogonal_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( ~ unorthogonal_lines(sk1,sk2)
& ~ distinct_lines(sk0,sk2)
& unorthogonal_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f20_nnf]) ).
cnf(c27,plain,
~ unorthogonal_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p28,plain,
convergent_lines(sk1,sk2),
inference(resolution,[status(thm)],[c17,c27]) ).
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]) ).
cnf(p31,plain,
( convergent_lines(sk2,X0)
| convergent_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p28,c5]) ).
cnf(p37,plain,
( convergent_lines(X0,X1)
| convergent_lines(sk2,X1)
| convergent_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p31,c5]) ).
fof(f11,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f11_nnf,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c13,plain,
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p63,plain,
( distinct_lines(X0,X1)
| convergent_lines(sk2,X1)
| convergent_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p37,c13]) ).
cnf(c26,plain,
~ distinct_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p257,plain,
( convergent_lines(sk2,sk2)
| convergent_lines(sk1,sk0) ),
inference(resolution,[status(thm)],[p63,c26]) ).
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(p272,plain,
convergent_lines(sk1,sk0),
inference(resolution,[status(thm)],[p257,c2]) ).
cnf(p297,plain,
( convergent_lines(sk0,X0)
| convergent_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p272,c5]) ).
cnf(p303,plain,
convergent_lines(sk0,sk1),
inference(resolution,[status(thm)],[p297,c2]) ).
fof(f16,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oac1) ).
fof(f16_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)],[f16]) ).
fof(f16_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)],[f16_nnf]) ).
cnf(c19,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p313,plain,
( unorthogonal_lines(sk1,X0)
| convergent_lines(sk0,X0)
| ~ unorthogonal_lines(sk0,sk1) ),
inference(resolution,[status(thm)],[p303,c19]) ).
cnf(c25,plain,
unorthogonal_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p722,plain,
( unorthogonal_lines(sk1,X0)
| convergent_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p313,c25]) ).
cnf(p723,plain,
convergent_lines(sk0,sk2),
inference(resolution,[status(thm)],[p722,c27]) ).
cnf(p726,plain,
distinct_lines(sk0,sk2),
inference(resolution,[status(thm)],[p723,c13]) ).
cnf(p733,plain,
$false,
inference(resolution,[status(thm)],[p726,c26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 11:32:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.70/1.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.70/1.12 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------