%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT040-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 26 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(absorption2,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption2) ).
cnf(c_4,plain,
join(A,meet(A,B)) = A,
inference(clausify,[status(thm)],[absorption2]) ).
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(commutativity_of_join,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_join) ).
cnf(c_6,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
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(lhs1,axiom,
join(xx,yy) = join(xx,zz),
file('theBenchmark.p',lhs1) ).
cnf(c_13,plain,
join(xx,yy) = join(xx,zz),
inference(clausify,[status(thm)],[lhs1]) ).
cnf(c_14,plain,
join(xx,zz) = join(xx,yy),
inference(copy,[status(thm)],[c_13]) ).
fof(lhs2,axiom,
meet(xx,yy) = meet(xx,zz),
file('theBenchmark.p',lhs2) ).
cnf(c_15,plain,
meet(xx,yy) = meet(xx,zz),
inference(clausify,[status(thm)],[lhs2]) ).
cnf(c_16,plain,
meet(xx,zz) = meet(xx,yy),
inference(copy,[status(thm)],[c_15]) ).
fof(rhs,axiom,
yy != zz,
file('theBenchmark.p',rhs) ).
cnf(c_17,plain,
yy != zz,
inference(clausify,[status(thm)],[rhs]) ).
cnf(c_18,plain,
zz != yy,
inference(copy,[status(thm)],[c_17]) ).
cnf(c_19,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_36,plain,
meet(join(A,B),join(B,C)) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_6,c_10]) ).
cnf(c_60,plain,
join(zz,meet(xx,yy)) = zz,
inference(paramod,[status(thm)],[c_16,c_19]) ).
cnf(c_69,plain,
meet(join(zz,xx),join(zz,yy)) = zz,
inference(paramod,[status(thm)],[c_60,c_10]) ).
cnf(c_70,plain,
meet(join(xx,zz),join(zz,yy)) = zz,
inference(paramod,[status(thm)],[c_6,c_69]) ).
cnf(c_71,plain,
meet(join(xx,yy),join(zz,yy)) = zz,
inference(paramod,[status(thm)],[c_14,c_70]) ).
cnf(c_72,plain,
meet(join(xx,yy),join(yy,zz)) = zz,
inference(paramod,[status(thm)],[c_6,c_71]) ).
cnf(c_73,plain,
join(yy,meet(xx,zz)) = zz,
inference(paramod,[status(thm)],[c_36,c_72]) ).
cnf(c_74,plain,
join(yy,meet(xx,yy)) = zz,
inference(paramod,[status(thm)],[c_16,c_73]) ).
cnf(c_75,plain,
yy = zz,
inference(paramod,[status(thm)],[c_19,c_74]) ).
cnf(c_76,plain,
zz = yy,
inference(copy,[status(thm)],[c_75]) ).
cnf(c_68,plain,
$false,
inference(resolve,[status(thm)],[c_18,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT040-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n007.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 19:56:53 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1739630 was started by sandbox2 on n007,
% 0.17/0.43 % Fri Sep 25 19:56:53 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 15.
% 0.17/0.45 % Level of proof is 3.
% 0.17/0.45 % Maximum clause weight is 28.000.
% 0.17/0.45 % Given clauses 16.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------