%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO210+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 : n018.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 01:17:31 PM UTC 2026
% Result : Theorem 6.17s 1.44s
% Output : Proof 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 20 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 48 ~; 60 |; 18 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 4 sgn 75 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,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/sandbox/benchmark/theBenchmark.p',oac1) ).
fof(f19_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)],[f19]) ).
fof(f19_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)],[f19_nnf]) ).
cnf(c20,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
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]) ).
fof(f20,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f20_nnf,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [L,A] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c23,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p49,plain,
convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[c18,c23]) ).
fof(f5,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/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]) ).
cnf(p50,plain,
( convergent_lines(X0,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[p49,c5]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/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(p68,plain,
convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(resolution,[status(thm)],[p50,c2]) ).
cnf(p116,plain,
( unorthogonal_lines(orthogonal_through_point(X0,X1),X2)
| convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1)) ),
inference(resolution,[status(thm)],[c20,p68]) ).
fof(f25,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',couo1) ).
fof(f25_nnf,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c31,plain,
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f31,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f31_nnf,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c39,plain,
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f35,conjecture,
! [A,L,M] :
( ( orthogonal_lines(L,M)
& incident_point_and_line(A,L) )
=> equal_lines(L,orthogonal_through_point(M,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [A,L,M] :
( ( orthogonal_lines(L,M)
& incident_point_and_line(A,L) )
=> equal_lines(L,orthogonal_through_point(M,A)) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [A,L,M] :
( ~ equal_lines(L,orthogonal_through_point(M,A))
& orthogonal_lines(L,M)
& incident_point_and_line(A,L) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ equal_lines(sk1,orthogonal_through_point(sk2,sk0))
& orthogonal_lines(sk1,sk2)
& incident_point_and_line(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f35_nnf]) ).
cnf(c48,plain,
~ equal_lines(sk1,orthogonal_through_point(sk2,sk0)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p51,plain,
distinct_lines(sk1,orthogonal_through_point(sk2,sk0)),
inference(resolution,[status(thm)],[c39,c48]) ).
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(p53,plain,
convergent_lines(sk1,orthogonal_through_point(sk2,sk0)),
inference(resolution,[status(thm)],[p51,c14]) ).
cnf(p146,plain,
( unorthogonal_lines(X0,orthogonal_through_point(sk2,sk0))
| unorthogonal_lines(X0,sk1) ),
inference(resolution,[status(thm)],[c31,p53]) ).
cnf(p982,plain,
( unorthogonal_lines(sk2,sk1)
| unorthogonal_lines(orthogonal_through_point(sk2,sk0),X0)
| convergent_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p116,p146]) ).
cnf(p4861,plain,
( unorthogonal_lines(sk2,sk1)
| convergent_lines(sk2,sk2) ),
inference(resolution,[status(thm)],[p982,c23]) ).
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]) ).
cnf(c47,plain,
orthogonal_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p58,plain,
~ unorthogonal_lines(sk1,sk2),
inference(resolution,[status(thm)],[c44,c47]) ).
cnf(p59,plain,
convergent_lines(sk1,sk2),
inference(resolution,[status(thm)],[p58,c18]) ).
cnf(p81,plain,
( convergent_lines(sk1,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[c13,p59]) ).
cnf(p86,plain,
distinct_lines(sk2,sk1),
inference(resolution,[status(thm)],[p81,c2]) ).
cnf(p92,plain,
convergent_lines(sk2,sk1),
inference(resolution,[status(thm)],[p86,c14]) ).
cnf(p119,plain,
( unorthogonal_lines(sk1,X0)
| convergent_lines(sk2,X0)
| ~ unorthogonal_lines(sk2,sk1) ),
inference(resolution,[status(thm)],[c20,p92]) ).
cnf(p4874,plain,
( unorthogonal_lines(sk1,X0)
| convergent_lines(sk2,X0)
| convergent_lines(sk2,sk2) ),
inference(resolution,[status(thm)],[p4861,p119]) ).
cnf(p4879,plain,
( unorthogonal_lines(sk1,sk2)
| convergent_lines(sk2,sk2) ),
inference(factoring,[status(thm)],[p4874]) ).
cnf(p4908,plain,
convergent_lines(sk2,sk2),
inference(resolution,[status(thm)],[p4879,p58]) ).
cnf(p4909,plain,
$false,
inference(resolution,[status(thm)],[p4908,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.56 % Computer : n018.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Wed Sep 23 11:32:33 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.56 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.17/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/1.44 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------