%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT012-1 : 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 : n002.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 07:49:32 AM UTC 2026
% Result : Unsatisfiable 0.23s 5.96s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 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 : 5 ( 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 : 49 ( 14 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mckenzie1,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,meet(VAR_1,meet(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',mckenzie1) ).
cnf(c_1,plain,
join(A,meet(B,meet(A,C))) = A,
inference(clausify,[status(thm)],[mckenzie1]) ).
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(mckenzie4,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(join(VAR_0,VAR_1),join(VAR_1,VAR_2)),VAR_1) = VAR_1,
file('theBenchmark.p',mckenzie4) ).
cnf(c_4,plain,
meet(meet(join(A,B),join(B,C)),B) = B,
inference(clausify,[status(thm)],[mckenzie4]) ).
fof(prove_commutativity_of_meet,axiom,
meet(b,a) != meet(a,b),
file('theBenchmark.p',prove_commutativity_of_meet) ).
cnf(c_5,plain,
meet(b,a) != meet(a,b),
inference(clausify,[status(thm)],[prove_commutativity_of_meet]) ).
cnf(c_6,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_7,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
join(meet(A,B),B) = B,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_14,plain,
join(A,meet(A,B)) = A,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_22,plain,
meet(meet(A,join(meet(B,A),C)),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_30,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_1245,plain,
join(meet(A,B),A) = join(A,meet(A,B)),
inference(paramod,[status(thm)],[c_14,c_30]) ).
cnf(c_62,plain,
join(meet(A,B),A) = A,
inference(paramod,[status(thm)],[c_14,c_1245]) ).
cnf(c_337,plain,
meet(meet(A,B),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_62,c_22]) ).
cnf(c_1242,plain,
join(meet(A,B),meet(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_337,c_14]) ).
cnf(c_1246,plain,
join(meet(A,B),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_337,c_62]) ).
cnf(c_1243,plain,
meet(A,B) = meet(B,A),
inference(paramod,[status(thm)],[c_1242,c_1246]) ).
cnf(c_1244,plain,
$false,
inference(resolve,[status(thm)],[c_1243,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT012-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.67 % Computer : n002.cluster.edu
% 0.19/5.67 % Model : x86_64 x86_64
% 0.19/5.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.67 % Memory : 8046.5625MB
% 0.19/5.67 % OS : Linux 6.8.0-71-generic
% 0.19/5.67 % CPULimit : 300
% 0.19/5.67 % WCLimit : 300
% 0.19/5.67 % DateTime : Fri Sep 25 19:58:56 UTC 2026
% 0.19/5.67 % CPUTime :
% 0.19/5.68 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.68 % Process 4011591 was started by sandbox2 on n002,
% 0.19/5.68 % Fri Sep 25 19:58:56 2026
% 0.19/5.68 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.68
% 0.19/5.68 % From the command line: assign(max_seconds, 300).
% 0.23/5.96
% 0.23/5.96 % SZS status Unsatisfiable for theBenchmark
% 0.23/5.96
% 0.23/5.96 % Proof 1 at 0.19 (+ 0.08) seconds.
% 0.23/5.96 % Length of proof is 16.
% 0.23/5.96 % Level of proof is 7.
% 0.23/5.96 % Maximum clause weight is 15.000.
% 0.23/5.96 % Given clauses 84.
% 0.23/5.96
% 0.23/5.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------