%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO233+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 07:17:37 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 12 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 24 ( 2 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(oag5,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('theBenchmark.p',oag5) ).
fof(oag6,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('theBenchmark.p',oag6) ).
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] : ~ unequally_directed_lines(reverse_line(reverse_line(L)),L),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L] : ~ unequally_directed_lines(reverse_line(reverse_line(L)),L),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_32,plain,
? [L] : unequally_directed_lines(reverse_line(reverse_line(L)),L),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
unequally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(L,sK0)],[nnf_32]) ).
cnf(c_73,negated_conjecture,
unequally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_87,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[oag11]) ).
cnf(c_90,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_128,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_87,c_90]) ).
cnf(c_91,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_87,c_128]) ).
cnf(c_93,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag6]) ).
cnf(c_94,plain,
~ unequally_directed_lines(A,A),
inference(clausify,[status(thm)],[oag5]) ).
cnf(c_102,negated_conjecture,
~ unequally_directed_lines(reverse_line(reverse_line(sK0)),reverse_line(sK0)),
inference(resolve,[status(thm)],[c_91,c_73]) ).
cnf(c_103,plain,
( unequally_directed_lines(sK0,A)
| unequally_directed_lines(reverse_line(reverse_line(sK0)),A) ),
inference(resolve,[status(thm)],[c_93,c_73]) ).
cnf(c_121,plain,
unequally_directed_lines(sK0,reverse_line(sK0)),
inference(resolve,[status(thm)],[c_103,c_102]) ).
cnf(c_122,plain,
unequally_directed_lines(sK0,reverse_line(reverse_line(sK0))),
inference(resolve,[status(thm)],[c_103,c_94]) ).
cnf(c_129,plain,
~ unequally_directed_lines(sK0,reverse_line(reverse_line(sK0))),
inference(resolve,[status(thm)],[c_91,c_121]) ).
cnf(c_127,plain,
$false,
inference(resolve,[status(thm)],[c_122,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO233+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n006.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 13:08:41 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 2997122 was started by sandbox on n006,
% 0.19/0.44 % Fri Sep 25 13:08:41 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % Assigning unary symbol reverse_line kb_weight 0 and highest precedence (12).
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.48 % Length of proof is 16.
% 0.19/0.48 % Level of proof is 5.
% 0.19/0.48 % Maximum clause weight is 28.000.
% 0.19/0.48 % Given clauses 26.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------