%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO216+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 : Sun Sep 27 07:17:32 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 12 ~; 2 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn 7 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(coipo1,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('theBenchmark.p',coipo1) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('theBenchmark.p',a5) ).
fof(con,conjecture,
! [L] : ~ orthogonal_lines(L,L),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L] : ~ orthogonal_lines(L,L),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_46,plain,
( ~ unorthogonal_lines(A,B)
| ~ orthogonal_lines(A,B) ),
inference(clausify,[status(thm)],[a5]) ).
fof(nnf_36,plain,
? [L] : orthogonal_lines(L,L),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
orthogonal_lines(sK0,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(L,sK0)],[nnf_36]) ).
cnf(c_47,negated_conjecture,
orthogonal_lines(sK0,sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
~ unorthogonal_lines(sK0,sK0),
inference(resolve,[status(thm)],[c_47,c_46]) ).
cnf(c_57,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[coipo1]) ).
cnf(c_80,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_84,negated_conjecture,
convergent_lines(sK0,sK0),
inference(resolve,[status(thm)],[c_57,c_48]) ).
cnf(c_83,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_80,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO216+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n008.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 13:07:39 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1118808 was started by sandbox on n008,
% 0.17/0.44 % Fri Sep 25 13:07:39 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.47
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47
% 0.17/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.47 % Length of proof is 10.
% 0.17/0.47 % Level of proof is 3.
% 0.17/0.47 % Maximum clause weight is 6.000.
% 0.17/0.47 % Given clauses 10.
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------