%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT014-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 07:49:33 AM UTC 2026
% Result : Unsatisfiable 0.07s 15.39s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 5 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mckenzie2,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,join(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',mckenzie2) ).
cnf(c_2,plain,
meet(A,join(B,join(A,C))) = A,
inference(clausify,[status(thm)],[mckenzie2]) ).
fof(mckenzie3,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet(VAR_0,VAR_1),meet(VAR_1,VAR_2)),VAR_1) = VAR_1,
file('theBenchmark.p',mckenzie3) ).
cnf(c_3,plain,
join(join(meet(A,B),meet(B,C)),B) = B,
inference(clausify,[status(thm)],[mckenzie3]) ).
fof(prove_absorbtion,axiom,
meet(a,join(a,b)) != a,
file('theBenchmark.p',prove_absorbtion) ).
cnf(c_5,plain,
meet(a,join(a,b)) != a,
inference(clausify,[status(thm)],[prove_absorbtion]) ).
cnf(c_10,plain,
meet(A,join(A,B)) = A,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT014-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.07/15.37 % CPULimit : 300
% 0.07/15.37 % WCLimit : 300
% 0.07/15.37 % DateTime : Fri Sep 25 19:57:57 UTC 2026
% 0.07/15.37 % CPUTime :
% 0.07/15.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/15.37 % Process 1747875 was started by sandbox2 on n008,
% 0.07/15.37 % Fri Sep 25 19:57:57 2026
% 0.07/15.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/15.37
% 0.07/15.37 % From the command line: assign(max_seconds, 300).
% 0.07/15.39
% 0.07/15.39 % SZS status Unsatisfiable for theBenchmark
% 0.07/15.39
% 0.07/15.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/15.39 % Length of proof is 5.
% 0.07/15.39 % Level of proof is 2.
% 0.07/15.39 % Maximum clause weight is 11.000.
% 0.07/15.39 % Given clauses 3.
% 0.07/15.39
% 0.07/15.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------