%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 07:17:46 AM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 16 ~; 19 |; 1 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 40 ( 2 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('theBenchmark.p',a1_defns) ).
fof(a5_defns,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('theBenchmark.p',a5_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_opposite_lines(L,reverse_line(L)),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L] : equally_directed_opposite_lines(L,reverse_line(L)),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_39,plain,
( unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a1_defns]) ).
cnf(c_41,plain,
( unequally_directed_opposite_lines(A,B)
| equally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a5_defns]) ).
cnf(c_55,plain,
( unequally_directed_lines(A,reverse_line(B))
| equally_directed_opposite_lines(A,B) ),
inference(resolve,[status(thm)],[c_41,c_39]) ).
fof(nnf_37,plain,
? [L] : ~ equally_directed_opposite_lines(L,reverse_line(L)),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
~ equally_directed_opposite_lines(sK0,reverse_line(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(L,sK0)],[nnf_37]) ).
cnf(c_57,negated_conjecture,
~ equally_directed_opposite_lines(sK0,reverse_line(sK0)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_106,negated_conjecture,
unequally_directed_lines(sK0,reverse_line(reverse_line(sK0))),
inference(resolve,[status(thm)],[c_57,c_55]) ).
cnf(c_111,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax6_basics]) ).
cnf(c_114,plain,
( unequally_directed_lines(A,reverse_line(B))
| unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax8_basics]) ).
cnf(c_115,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_117,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[ax11_basics]) ).
cnf(c_147,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_117,c_115]) ).
cnf(c_132,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_117,c_147]) ).
cnf(c_134,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| unequally_directed_lines(A,reverse_line(B)) ),
inference(resolve,[status(thm)],[c_114,c_111]) ).
cnf(c_148,plain,
( unequally_directed_lines(A,reverse_line(A))
| unequally_directed_lines(A,reverse_line(A)) ),
inference(factor,[status(thm)],[c_134]) ).
cnf(c_137,plain,
unequally_directed_lines(A,reverse_line(A)),
inference(copy,[status(thm)],[c_148]) ).
cnf(c_149,negated_conjecture,
~ unequally_directed_lines(sK0,reverse_line(sK0)),
inference(resolve,[status(thm)],[c_132,c_106]) ).
cnf(c_146,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_137,c_149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 13:07:17 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 2347542 was started by sandbox2 on n017,
% 0.09/0.37 % Fri Sep 25 13:07:17 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.41
% 0.09/0.41 % SZS status Theorem for theBenchmark
% 0.09/0.41
% 0.09/0.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.41 % Length of proof is 20.
% 0.09/0.41 % Level of proof is 4.
% 0.09/0.41 % Maximum clause weight is 24.000.
% 0.09/0.41 % Given clauses 18.
% 0.09/0.41
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------