%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT039-2 : TPTP v9.3.1. Released v2.4.0.
% 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 07:49:36 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 def)
% Number of atoms : 7 ( 6 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dist_join,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,meet(VAR_1,VAR_2)) = meet(join(VAR_0,VAR_1),join(VAR_0,VAR_2)),
file('theBenchmark.p',dist_join) ).
cnf(c_9,plain,
join(A,meet(B,C)) = meet(join(A,B),join(A,C)),
inference(clausify,[status(thm)],[dist_join]) ).
cnf(c_10,plain,
meet(join(A,B),join(A,C)) = join(A,meet(B,C)),
inference(copy,[status(thm)],[c_9]) ).
fof(rhs,axiom,
join(xx,meet(yy,zz)) != meet(join(xx,yy),join(xx,zz)),
file('theBenchmark.p',rhs) ).
cnf(c_13,plain,
join(xx,meet(yy,zz)) != meet(join(xx,yy),join(xx,zz)),
inference(clausify,[status(thm)],[rhs]) ).
cnf(c_15,plain,
meet(join(xx,yy),join(xx,zz)) != join(xx,meet(yy,zz)),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT039-2 : TPTP v9.3.1. Released v2.4.0.
% 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 19:58:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 963155 was started by sandbox on n014,
% 0.09/0.37 % Fri Sep 25 19:58:34 2026
% 0.09/0.37 % 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 Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 4.
% 0.09/0.38 % Level of proof is 2.
% 0.09/0.38 % Maximum clause weight is 28.000.
% 0.09/0.38 % Given clauses 0.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------