%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO220+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:17:33 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 32 ( 19 ~; 3 |; 7 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('theBenchmark.p',couo1) ).
fof(con,conjecture,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_36,plain,
( ~ convergent_lines(B,C)
| unorthogonal_lines(A,C)
| unorthogonal_lines(A,B) ),
inference(clausify,[status(thm)],[couo1]) ).
fof(nnf_16,plain,
? [L,M,N] :
( convergent_lines(M,N)
& ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( convergent_lines(sK1,sK2)
& ~ unorthogonal_lines(sK0,sK2)
& ~ unorthogonal_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(L,sK0),skolemize(M,sK1),skolemize(N,sK2)],[nnf_16]) ).
cnf(c_37,negated_conjecture,
~ unorthogonal_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_38,negated_conjecture,
~ unorthogonal_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_39,negated_conjecture,
convergent_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_43,negated_conjecture,
( ~ convergent_lines(sK1,A)
| unorthogonal_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_36,c_37]) ).
cnf(c_44,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_43,c_38]) ).
cnf(c_42,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_39,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO220+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:07:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 495667 was started by sandbox2 on n013,
% 0.09/0.37 % Fri Sep 25 13:07:21 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 7.
% 0.09/0.40 % Level of proof is 2.
% 0.09/0.40 % Maximum clause weight is 14.000.
% 0.09/0.40 % Given clauses 21.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------