%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO233+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 : 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 07:17:37 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 15 ~; 17 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 34 ( 2 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a4_defns,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('theBenchmark.p',a4_defns) ).
fof(ax6_basics,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('theBenchmark.p',ax6_basics) ).
fof(ax8_basics,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('theBenchmark.p',ax8_basics) ).
fof(ax9_basics,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',ax9_basics) ).
fof(ax11_basics,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('theBenchmark.p',ax11_basics) ).
fof(con,conjecture,
! [L] : equally_directed_lines(reverse_line(reverse_line(L)),L),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L] : equally_directed_lines(reverse_line(reverse_line(L)),L),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_46,plain,
( unequally_directed_lines(A,B)
| equally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[a4_defns]) ).
fof(nnf_37,plain,
? [L] : ~ equally_directed_lines(reverse_line(reverse_line(L)),L),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
~ equally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(L,sK0)],[nnf_37]) ).
cnf(c_53,negated_conjecture,
~ equally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_108,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax6_basics]) ).
cnf(c_111,plain,
( unequally_directed_lines(A,reverse_line(B))
| unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax8_basics]) ).
cnf(c_112,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)],[ax9_basics]) ).
cnf(c_114,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[ax11_basics]) ).
cnf(c_129,negated_conjecture,
unequally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(resolve,[status(thm)],[c_53,c_46]) ).
cnf(c_140,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_114,c_112]) ).
cnf(c_130,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_114,c_140]) ).
cnf(c_131,plain,
( unequally_directed_lines(reverse_line(B),C)
| unequally_directed_lines(A,C)
| unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_111,c_108]) ).
cnf(c_141,plain,
( unequally_directed_lines(reverse_line(A),A)
| unequally_directed_lines(reverse_line(A),A) ),
inference(factor,[status(thm)],[c_131]) ).
cnf(c_133,plain,
unequally_directed_lines(reverse_line(A),A),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_142,negated_conjecture,
~ unequally_directed_lines(reverse_line(reverse_line(sK0)),reverse_line(sK0)),
inference(resolve,[status(thm)],[c_130,c_129]) ).
cnf(c_139,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_133,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO233+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.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 13:08:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 294008 was started by sandbox on n014,
% 0.09/0.36 % Fri Sep 25 13:08:47 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 17.
% 0.09/0.38 % Level of proof is 4.
% 0.09/0.38 % Maximum clause weight is 14.000.
% 0.09/0.38 % Given clauses 18.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------