%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO267+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 : n018.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 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 14 ~; 8 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 25 ( 0 sgn 12 !; 3 ?)
% 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(ax8_basics,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('theBenchmark.p',ax8_basics) ).
fof(con,conjecture,
! [L,M,N] :
( unequally_directed_opposite_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_opposite_lines(M,N) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( unequally_directed_opposite_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_opposite_lines(M,N) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_38,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| unequally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a1_defns]) ).
cnf(c_40,plain,
( ~ unequally_directed_opposite_lines(A,B)
| ~ equally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a5_defns]) ).
cnf(c_41,plain,
( unequally_directed_opposite_lines(A,B)
| equally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a5_defns]) ).
fof(nnf_37,plain,
? [L,M,N] :
( ~ unequally_directed_lines(M,N)
& ~ unequally_directed_opposite_lines(M,N)
& unequally_directed_opposite_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ unequally_directed_lines(sK0,sK1)
& ~ unequally_directed_opposite_lines(sK0,sK1)
& unequally_directed_opposite_lines(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(L,sK2),skolemize(M,sK0),skolemize(N,sK1)],[nnf_37]) ).
cnf(c_45,negated_conjecture,
~ unequally_directed_opposite_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_56,negated_conjecture,
equally_directed_opposite_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_60,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ equally_directed_opposite_lines(A,B) ),
inference(resolve,[status(thm)],[c_40,c_38]) ).
cnf(c_111,negated_conjecture,
~ unequally_directed_lines(sK0,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_60,c_56]) ).
cnf(c_120,plain,
( unequally_directed_lines(A,reverse_line(B))
| unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax8_basics]) ).
cnf(c_135,negated_conjecture,
~ unequally_directed_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_143,negated_conjecture,
unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_120,c_111]) ).
cnf(c_142,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_135,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO267+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n018.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Fri Sep 25 13:14:06 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 2039679 was started by sandbox2 on n018,
% 0.17/0.45 % Fri Sep 25 13:14:06 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 0.17/0.49
% 0.17/0.49 % Assigning unary symbol reverse_line kb_weight 0 and highest precedence (15).
% 0.17/0.49
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49
% 0.17/0.49 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.49 % Length of proof is 14.
% 0.17/0.49 % Level of proof is 4.
% 0.17/0.49 % Maximum clause weight is 17.000.
% 0.17/0.49 % Given clauses 8.
% 0.17/0.49
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------