%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO228+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 07:17:36 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 27 ~; 26 |; 8 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 24 ( 2 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con_def,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) ) ),
file('theBenchmark.p',con_def) ).
fof(oag9,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('theBenchmark.p',oag9) ).
fof(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('theBenchmark.p',oag11) ).
fof(con,conjecture,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_32,plain,
? [L,M] :
( ( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
| convergent_lines(L,M) )
& ( ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| ~ convergent_lines(L,M) ) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg_sk,plain,
( ( ( unequally_directed_lines(sK0,reverse_line(sK1))
& unequally_directed_lines(sK0,sK1) )
| convergent_lines(sK0,sK1) )
& ( ~ unequally_directed_lines(sK0,reverse_line(sK1))
| ~ unequally_directed_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(L,sK0),skolemize(M,sK1)],[nnf_32]) ).
fof(sk_con_neg,plain,
( ( unequally_directed_lines(sK0,reverse_line(sK1))
| convergent_lines(sK0,sK1) )
& ( unequally_directed_lines(sK0,sK1)
| convergent_lines(sK0,sK1) )
& ( ~ unequally_directed_lines(sK0,reverse_line(sK1))
| ~ unequally_directed_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_con_neg_sk]) ).
cnf(c_42,negated_conjecture,
( unequally_directed_lines(sK0,sK1)
| convergent_lines(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_43,negated_conjecture,
( unequally_directed_lines(sK0,reverse_line(sK1))
| convergent_lines(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_45,plain,
( unequally_directed_lines(A,reverse_line(B))
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con_def]) ).
cnf(c_46,plain,
( unequally_directed_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con_def]) ).
cnf(c_89,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[oag11]) ).
cnf(c_92,plain,
( left_convergent_lines(A,reverse_line(B))
| left_convergent_lines(A,B)
| ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag9]) ).
cnf(c_118,plain,
( left_convergent_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_89,c_92]) ).
cnf(c_93,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_89,c_118]) ).
cnf(c_103,negated_conjecture,
( unequally_directed_lines(sK0,reverse_line(sK1))
| unequally_directed_lines(sK0,reverse_line(sK1)) ),
inference(resolve,[status(thm)],[c_45,c_43]) ).
cnf(c_104,negated_conjecture,
unequally_directed_lines(sK0,reverse_line(sK1)),
inference(copy,[status(thm)],[c_103]) ).
cnf(c_105,negated_conjecture,
( unequally_directed_lines(sK0,sK1)
| unequally_directed_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_46,c_42]) ).
cnf(c_106,negated_conjecture,
unequally_directed_lines(sK0,sK1),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_119,negated_conjecture,
~ unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_104,c_93]) ).
cnf(c_117,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_106,c_119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO228+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n014.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 13:08:32 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 293117 was started by sandbox2 on n014,
% 0.09/0.35 % Fri Sep 25 13:08:32 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 16.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 7.000.
% 0.09/0.39 % Given clauses 17.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------