%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO213+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 5.47s 1.16s
% Output : Proof 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 18 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 31 ~; 47 |; 11 &)
% ( 0 <=>; 6 =>; 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 : 81 ( 0 sgn 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( convergent_lines(X0,X2)
| distinct_lines(X1,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',ax6) ).
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(f17,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
fof(f17_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f22,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(f22_neg,negated_conjecture,
~ ! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ distinct_lines(L,N)
& unorthogonal_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
( ~ unorthogonal_lines(sk1,sk2)
& ~ distinct_lines(sk0,sk2)
& unorthogonal_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f22_nnf]) ).
cnf(c27,plain,
~ unorthogonal_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p28,plain,
convergent_lines(sk1,sk2),
inference(resolution,[status(thm)],[c17,c27]) ).
cnf(p30,plain,
( convergent_lines(sk2,X0)
| convergent_lines(sk1,X0) ),
inference(resolution,[status(thm)],[c5,p28]) ).
cnf(p47,plain,
( convergent_lines(sk1,X0)
| convergent_lines(sk2,X1)
| distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[c13,p30]) ).
cnf(c26,plain,
~ distinct_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p144,plain,
( convergent_lines(sk1,sk0)
| convergent_lines(sk2,sk2) ),
inference(resolution,[status(thm)],[p47,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(p181,plain,
convergent_lines(sk1,sk0),
inference(resolution,[status(thm)],[p144,c2]) ).
cnf(p182,plain,
( convergent_lines(sk0,X0)
| convergent_lines(sk1,X0) ),
inference(resolution,[status(thm)],[p181,c5]) ).
cnf(p213,plain,
convergent_lines(sk0,sk1),
inference(resolution,[status(thm)],[p182,c2]) ).
fof(f18,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(f18_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)],[f18]) ).
fof(f18_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)],[f18_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)],[f18_sk]) ).
cnf(p224,plain,
( unorthogonal_lines(sk1,X0)
| convergent_lines(sk0,X0)
| ~ unorthogonal_lines(sk0,sk1) ),
inference(resolution,[status(thm)],[p213,c19]) ).
cnf(c25,plain,
unorthogonal_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p907,plain,
( unorthogonal_lines(sk1,X0)
| convergent_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p224,c25]) ).
cnf(p908,plain,
convergent_lines(sk0,sk2),
inference(resolution,[status(thm)],[p907,c27]) ).
cnf(p916,plain,
( convergent_lines(sk0,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p908,c13]) ).
cnf(p927,plain,
distinct_lines(sk2,sk0),
inference(resolution,[status(thm)],[p916,c2]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p935,plain,
( distinct_lines(sk0,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p927,c4]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
fof(f1_nnf,plain,
! [X] : ~ distinct_lines(X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ distinct_lines(X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p938,plain,
distinct_lines(sk0,sk2),
inference(resolution,[status(thm)],[p935,c1]) ).
cnf(p942,plain,
$false,
inference(resolution,[status(thm)],[p938,c26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO213+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n005.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 11:31:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.47/1.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.47/1.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------