%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 2.69s 0.79s
% Output : Proof 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 16 unt; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 46 ~; 49 |; 15 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 87 ( 0 sgn 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,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/sandbox/benchmark/theBenchmark.p',cotno1) ).
fof(f24_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)],[f24]) ).
fof(f24_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)],[f24_nnf]) ).
cnf(c28,plain,
( ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/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(f34,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
fof(f34_nnf,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c44,plain,
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
fof(f35,conjecture,
! [L,M,N] :
( ( orthogonal_lines(L,N)
& parallel_lines(L,M) )
=> orthogonal_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [L,M,N] :
( ( orthogonal_lines(L,N)
& parallel_lines(L,M) )
=> orthogonal_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [L,M,N] :
( ~ orthogonal_lines(M,N)
& orthogonal_lines(L,N)
& parallel_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ orthogonal_lines(sk1,sk2)
& orthogonal_lines(sk0,sk2)
& parallel_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f35_nnf]) ).
cnf(c47,plain,
orthogonal_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p52,plain,
~ unorthogonal_lines(sk0,sk2),
inference(resolution,[status(thm)],[c44,c47]) ).
fof(f18,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f18_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p54,plain,
convergent_lines(sk0,sk2),
inference(resolution,[status(thm)],[p52,c18]) ).
cnf(p70,plain,
( convergent_lines(sk0,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[c13,p54]) ).
fof(f32,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
fof(f32_nnf,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c40,plain,
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(c46,plain,
parallel_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p51,plain,
~ convergent_lines(sk0,sk1),
inference(resolution,[status(thm)],[c40,c46]) ).
cnf(p76,plain,
distinct_lines(sk2,sk1),
inference(resolution,[status(thm)],[p70,p51]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox/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(p82,plain,
( distinct_lines(sk1,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p76,c4]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/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(p99,plain,
distinct_lines(sk1,sk2),
inference(resolution,[status(thm)],[p82,c1]) ).
fof(f14,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f14_nnf,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p101,plain,
convergent_lines(sk1,sk2),
inference(resolution,[status(thm)],[p99,c14]) ).
cnf(p182,plain,
( ~ unorthogonal_lines(sk1,sk2)
| unorthogonal_lines(X0,sk2)
| convergent_lines(X0,sk1) ),
inference(resolution,[status(thm)],[c28,p101]) ).
cnf(c45,plain,
( unorthogonal_lines(X0,X1)
| orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(c48,plain,
~ orthogonal_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p57,plain,
unorthogonal_lines(sk1,sk2),
inference(resolution,[status(thm)],[c45,c48]) ).
cnf(p1126,plain,
( unorthogonal_lines(X0,sk2)
| convergent_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p182,p57]) ).
cnf(p1128,plain,
convergent_lines(sk0,sk1),
inference(resolution,[status(thm)],[p1126,p52]) ).
cnf(p1133,plain,
$false,
inference(resolution,[status(thm)],[p1128,p51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 11:35:08 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.69/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.69/0.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------