%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO221+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 01:17:35 PM UTC 2026
% Result : Theorem 13.20s 2.25s
% Output : Proof 13.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 15 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 36 ~; 47 |; 12 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 108 ( 10 sgn 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
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(p48,plain,
convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[c18,c23]) ).
cnf(p49,plain,
( convergent_lines(X0,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[c5,p48]) ).
cnf(p60,plain,
( convergent_lines(X1,X3)
| convergent_lines(orthogonal_through_point(X0,X2),X3)
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[p49,c5]) ).
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]) ).
cnf(p143,plain,
( unorthogonal_lines(X4,X3)
| unorthogonal_lines(X4,X0)
| convergent_lines(X3,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[p60,c31]) ).
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(p2131,plain,
( unorthogonal_lines(X3,X0)
| unorthogonal_lines(X3,X1)
| convergent_lines(X0,orthogonal_through_point(X1,X2)) ),
inference(resolution,[status(thm)],[p143,c2]) ).
cnf(p2835,plain,
( unorthogonal_lines(orthogonal_through_point(X1,X3),X0)
| convergent_lines(X0,orthogonal_through_point(X1,X2)) ),
inference(resolution,[status(thm)],[p2131,c23]) ).
cnf(p2882,plain,
unorthogonal_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2)),
inference(resolution,[status(thm)],[p2835,c2]) ).
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(c22,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f35,conjecture,
! [A,B,L] :
( incident_point_and_line(B,orthogonal_through_point(L,A))
=> equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [A,B,L] :
( incident_point_and_line(B,orthogonal_through_point(L,A))
=> equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [A,B,L] :
( ~ equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B))
& incident_point_and_line(B,orthogonal_through_point(L,A)) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ equal_lines(orthogonal_through_point(sk2,sk0),orthogonal_through_point(sk2,sk1))
& incident_point_and_line(sk1,orthogonal_through_point(sk2,sk0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f35_nnf]) ).
cnf(c47,plain,
~ equal_lines(orthogonal_through_point(sk2,sk0),orthogonal_through_point(sk2,sk1)),
inference(cnf_transformation,[status(esa)],[f35_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]) ).
cnf(p51,plain,
distinct_lines(orthogonal_through_point(sk2,sk0),orthogonal_through_point(sk2,sk1)),
inference(resolution,[status(thm)],[c47,c39]) ).
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(p54,plain,
convergent_lines(orthogonal_through_point(sk2,sk0),orthogonal_through_point(sk2,sk1)),
inference(resolution,[status(thm)],[p51,c14]) ).
cnf(p120,plain,
( unorthogonal_lines(orthogonal_through_point(sk2,sk1),X0)
| unorthogonal_lines(orthogonal_through_point(sk2,sk0),X0)
| ~ unorthogonal_lines(orthogonal_through_point(sk2,sk0),orthogonal_through_point(sk2,sk1)) ),
inference(resolution,[status(thm)],[c22,p54]) ).
cnf(p2982,plain,
( unorthogonal_lines(orthogonal_through_point(sk2,sk1),X0)
| unorthogonal_lines(orthogonal_through_point(sk2,sk0),X0) ),
inference(resolution,[status(thm)],[p2882,p120]) ).
cnf(p3110,plain,
unorthogonal_lines(orthogonal_through_point(sk2,sk0),sk2),
inference(resolution,[status(thm)],[p2982,c23]) ).
cnf(p3131,plain,
$false,
inference(resolution,[status(thm)],[p3110,c23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO221+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 11:35:32 UTC 2026
% 0.01/0.38 % CPUTime :
% 0.01/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.20/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.20/2.25 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------