%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT042-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(absorption1,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption1) ).
cnf(c_3,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption1]) ).
fof(commutativity_of_meet,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = meet(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_meet) ).
cnf(c_5,plain,
meet(A,B) = meet(B,A),
inference(clausify,[status(thm)],[commutativity_of_meet]) ).
fof(distributivity,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,VAR_2)) = join(meet(VAR_0,VAR_1),meet(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity) ).
cnf(c_9,plain,
meet(A,join(B,C)) = join(meet(A,B),meet(A,C)),
inference(clausify,[status(thm)],[distributivity]) ).
cnf(c_10,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_9]) ).
fof(prove_modular_law,axiom,
join(a,meet(b,join(a,c))) != meet(join(a,b),join(a,c)),
file('theBenchmark.p',prove_modular_law) ).
cnf(c_14,plain,
join(a,meet(b,join(a,c))) != meet(join(a,b),join(a,c)),
inference(clausify,[status(thm)],[prove_modular_law]) ).
cnf(c_15,plain,
meet(join(A,B),A) = A,
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_82,plain,
join(a,meet(join(a,c),b)) != meet(join(a,b),join(a,c)),
inference(paramod,[status(thm)],[c_5,c_14]) ).
cnf(c_94,plain,
join(A,meet(join(A,B),C)) = meet(join(A,B),join(A,C)),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_118,plain,
join(a,meet(join(a,c),b)) != meet(join(a,c),join(a,b)),
inference(paramod,[status(thm)],[c_5,c_82]) ).
cnf(c_117,plain,
$false,
inference(resolve,[status(thm)],[c_94,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT042-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 19:58:51 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 3953404 was started by sandbox2 on n004,
% 0.10/0.35 % Fri Sep 25 19:58:51 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 9.
% 0.13/0.38 % Level of proof is 3.
% 0.13/0.38 % Maximum clause weight is 35.000.
% 0.13/0.38 % Given clauses 17.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------