%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT008-1 : 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 : n011.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 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 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 : 54 ( 9 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(absorption,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption) ).
cnf(c_1,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption]) ).
fof(distribution,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,VAR_2)) = join(meet(VAR_2,VAR_0),meet(VAR_1,VAR_0)),
file('theBenchmark.p',distribution) ).
cnf(c_2,plain,
meet(A,join(B,C)) = join(meet(C,A),meet(B,A)),
inference(clausify,[status(thm)],[distribution]) ).
fof(prove_absorbtion_dual,axiom,
join(a,meet(a,b)) != a,
file('theBenchmark.p',prove_absorbtion_dual) ).
cnf(c_3,plain,
join(a,meet(a,b)) != a,
inference(clausify,[status(thm)],[prove_absorbtion_dual]) ).
cnf(c_4,plain,
join(meet(A,B),meet(B,B)) = B,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_6,plain,
meet(join(A,B),join(C,A)) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_9,plain,
join(A,meet(join(A,B),join(A,B))) = join(A,B),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_92,plain,
meet(A,B) = join(meet(meet(B,B),A),meet(meet(C,B),A)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_10,plain,
join(meet(meet(A,A),B),meet(meet(C,A),B)) = meet(B,A),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_93,plain,
join(A,join(A,meet(A,join(A,A)))) = join(A,A),
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_24,plain,
join(A,join(A,A)) = join(A,A),
inference(paramod,[status(thm)],[c_1,c_93]) ).
cnf(c_94,plain,
join(meet(A,A),meet(meet(B,A),A)) = meet(A,A),
inference(paramod,[status(thm)],[c_8,c_10]) ).
cnf(c_37,plain,
join(meet(A,A),meet(B,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_8,c_94]) ).
cnf(c_95,plain,
meet(A,join(B,B)) = join(meet(join(B,B),A),meet(B,A)),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_38,plain,
join(meet(join(A,A),B),meet(A,B)) = meet(B,join(A,A)),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_96,plain,
join(meet(A,A),A) = join(meet(A,A),meet(A,A)),
inference(paramod,[status(thm)],[c_4,c_24]) ).
cnf(c_40,plain,
join(meet(A,A),A) = meet(A,A),
inference(paramod,[status(thm)],[c_37,c_96]) ).
cnf(c_97,plain,
join(meet(A,A),join(meet(A,A),meet(A,A))) = A,
inference(paramod,[status(thm)],[c_4,c_24]) ).
cnf(c_98,plain,
join(meet(A,A),meet(A,A)) = A,
inference(paramod,[status(thm)],[c_37,c_97]) ).
cnf(c_41,plain,
meet(A,A) = A,
inference(paramod,[status(thm)],[c_37,c_98]) ).
cnf(c_99,plain,
join(A,A) = meet(A,A),
inference(paramod,[status(thm)],[c_41,c_40]) ).
cnf(c_45,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_41,c_99]) ).
cnf(c_100,plain,
join(A,meet(B,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_41,c_37]) ).
cnf(c_46,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_41,c_100]) ).
cnf(c_101,plain,
join(meet(A,B),meet(A,B)) = meet(B,join(A,A)),
inference(paramod,[status(thm)],[c_45,c_38]) ).
cnf(c_102,plain,
meet(A,B) = meet(B,join(A,A)),
inference(paramod,[status(thm)],[c_45,c_101]) ).
cnf(c_53,plain,
meet(A,B) = meet(B,A),
inference(paramod,[status(thm)],[c_45,c_102]) ).
cnf(c_90,plain,
join(A,meet(A,B)) = A,
inference(paramod,[status(thm)],[c_53,c_46]) ).
cnf(c_91,plain,
$false,
inference(resolve,[status(thm)],[c_90,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT008-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 19:56:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2739832 was started by sandbox2 on n011,
% 0.11/0.38 % Fri Sep 25 19:56:43 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.40 % Length of proof is 18.
% 0.11/0.40 % Level of proof is 8.
% 0.11/0.40 % Maximum clause weight is 27.000.
% 0.11/0.40 % Given clauses 20.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------